Sorting algorithms/Merge sort
You are encouraged to solve this task according to the task description, using any language you may know.
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
The merge sort is a recursive sort of order n*log(n).
It is notable for having a worst case and average complexity of O(n*log(n)), and a best case complexity of O(n) (for pre-sorted input).
The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups).
Then merge the groups back together so that their elements are in order.
This is how the algorithm gets its divide and conquer description.
- Task
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts: a sort function and a merge function.
The functions in pseudocode look like this:
function mergesort(m)
var list left, right, result
if length(m) ≤ 1
return m
else
var middle = length(m) / 2
for each x in m up to middle - 1
add x to left
for each x in m at and after middle
add x to right
left = mergesort(left)
right = mergesort(right)
if last(left) ≤ first(right)
append right to left
return left
result = merge(left, right)
return result
function merge(left,right)
var list result
while length(left) > 0 and length(right) > 0
if first(left) ≤ first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
if length(left) > 0
append rest(left) to result
if length(right) > 0
append rest(right) to result
return result
For more information see the Wikipedia entry: merge sort.
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates example code, so is not shown here.
360 Assembly
The program uses ASM structured macros and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible. <lang 360asm>* Merge sort 19/06/2016 MAIN CSECT
STM R14,R12,12(R13) save caller's registers
LR R12,R15 set R12 as base register
USING MAIN,R12 notify assembler
LA R11,SAVEXA get the address of my savearea
ST R13,4(R11) save caller's save area pointer
ST R11,8(R13) save my save area pointer
LR R13,R11 set R13 to point to my save area
LA R1,1 1
LA R2,NN hbound(a)
BAL R14,SPLIT call split(1,hbound(a))
LA RPGI,PG pgi=0
LA RI,1 i=1
DO WHILE=(C,RI,LE,=A(NN)) do i=1 to hbound(a)
LR R1,RI i
SLA R1,2 .
L R2,A-4(R1) a(i)
XDECO R2,XDEC edit a(i)
MVC 0(4,RPGI),XDEC+8 output a(i)
LA RPGI,4(RPGI) pgi=pgi+4
LA RI,1(RI) i=i+1
ENDDO , end do
XPRNT PG,80 print buffer
L R13,SAVEXA+4 restore caller's savearea address
LM R14,R12,12(R13) restore caller's registers
XR R15,R15 set return code to 0
BR R14 return to caller
- split(istart,iend) ------recursive---------------------
SPLIT STM R14,R12,12(R13) save all registers
LR R9,R1 save R1
LA R1,72 amount of storage required
GETMAIN RU,LV=(R1) allocate storage for stack
USING STACK,R10 make storage addressable
LR R10,R1 establish stack addressability
LA R11,SAVEXB get the address of my savearea
ST R13,4(R11) save caller's save area pointer
ST R11,8(R13) save my save area pointer
LR R13,R11 set R13 to point to my save area
LR R1,R9 restore R1
LR RSTART,R1 istart=R1
LR REND,R2 iend=R2
IF CR,REND,EQ,RSTART THEN if iend=istart
B RETURN return
ENDIF , end if
BCTR R2,0 iend-1
IF C,R2,EQ,RSTART THEN if iend-istart=1
LR R1,REND iend
SLA R1,2 .
L R2,A-4(R1) a(iend)
LR R1,RSTART istart
SLA R1,2 .
L R3,A-4(R1) a(istart)
IF CR,R2,LT,R3 THEN if a(iend)<a(istart)
LR R1,RSTART istart
SLA R1,2 .
LA R2,A-4(R1) @a(istart)
LR R1,REND iend
SLA R1,2 .
LA R3,A-4(R1) @a(iend)
MVC TEMP,0(R2) temp=a(istart)
MVC 0(4,R2),0(R3) a(istart)=a(iend)
MVC 0(4,R3),TEMP a(iend)=temp
ENDIF , end if
B RETURN return
ENDIF , end if
LR RMIDDL,REND iend
SR RMIDDL,RSTART iend-istart
SRA RMIDDL,1 (iend-istart)/2
AR RMIDDL,RSTART imiddl=istart+(iend-istart)/2
LR R1,RSTART istart
LR R2,RMIDDL imiddl
BAL R14,SPLIT call split(istart,imiddl)
LA R1,1(RMIDDL) imiddl+1
LR R2,REND iend
BAL R14,SPLIT call split(imiddl+1,iend)
LR R1,RSTART istart
LR R2,RMIDDL imiddl
LR R3,REND iend
BAL R14,MERGE call merge(istart,imiddl,iend)
RETURN L R13,SAVEXB+4 restore caller's savearea address
XR R15,R15 set return code to 0
LA R0,72 amount of storage to free
FREEMAIN A=(R10),LV=(R0) free allocated storage
L R14,12(R13) restore caller's return address
LM R2,R12,28(R13) restore registers R2 to R12
BR R14 return to caller
DROP R10 base no longer needed
- merge(jstart,jmiddl,jend) ------------------------------------
MERGE STM R1,R3,JSTART jstart=r1,jmiddl=r2,jend=r3
SR R2,R1 jmiddl-jstart
LA RBS,2(R2) bs=jmiddl-jstart+2
LA RI,1 i=1
LR R3,RBS bs
BCTR R3,0 bs-1
DO WHILE=(CR,RI,LE,R3) do i=0 to bs-1
L R2,JSTART jstart
AR R2,RI jstart+i
SLA R2,2 .
L R2,A-8(R2) a(jstart+i-1)
LR R1,RI i
SLA R1,2 .
ST R2,B-4(R1) b(i)=a(jstart+i-1)
LA RI,1(RI) i=i+1
ENDDO , end do
LA RI,1 i=1
L RJ,JMIDDL j=jmiddl
LA RJ,1(RJ) j=jmiddl+1
L RK,JSTART k=jstart
DO UNTIL=(CR,RI,EQ,RBS,OR, do until i=bs or X
C,RJ,GT,JEND) j>jend
LR R1,RI i
SLA R1,2 .
L R4,B-4(R1) r4=b(i)
LR R1,RJ j
SLA R1,2 .
L R3,A-4(R1) r3=a(j)
LR R9,RK k
SLA R9,2 r9 for a(k)
IF CR,R4,LE,R3 THEN if b(i)<=a(j)
ST R4,A-4(R9) a(k)=b(i)
LA RI,1(RI) i=i+1
ELSE , else
ST R3,A-4(R9) a(k)=a(j)
LA RJ,1(RJ) j=j+1
ENDIF , end if
LA RK,1(RK) k=k+1
ENDDO , end do
DO WHILE=(CR,RI,LT,RBS) do while i<bs
LR R1,RI i
SLA R1,2 .
L R2,B-4(R1) b(i)
LR R1,RK k
SLA R1,2 .
ST R2,A-4(R1) a(k)=b(i)
LA RI,1(RI) i=i+1
LA RK,1(RK) k=k+1
ENDDO , end do
BR R14 return to caller
- ------- ------------------ ------------------------------------
LTORG
SAVEXA DS 18F savearea of main NN EQU ((B-A)/L'A) number of items A DC F'4',F'65',F'2',F'-31',F'0',F'99',F'2',F'83',F'782',F'1'
DC F'45',F'82',F'69',F'82',F'104',F'58',F'88',F'112',F'89',F'74'
B DS (NN/2+1)F merge sort static storage TEMP DS F for swap JSTART DS F jstart JMIDDL DS F jmiddl JEND DS F jend PG DC CL80' ' buffer XDEC DS CL12 for edit STACK DSECT dynamic area SAVEXB DS 18F " savearea of mergsort (72 bytes)
YREGS
RI EQU 6 i RJ EQU 7 j RK EQU 8 k RSTART EQU 6 istart REND EQU 7 i RMIDDL EQU 8 i RPGI EQU 3 pgi RBS EQU 0 bs
END MAIN</lang>
- Output:
-31 0 1 2 2 4 45 58 65 69 74 82 82 83 88 89 99 104 112 782
ACL2
<lang Lisp>(defun split (xys)
(if (endp (rest xys))
(mv xys nil)
(mv-let (xs ys)
(split (rest (rest xys)))
(mv (cons (first xys) xs)
(cons (second xys) ys)))))
(defun mrg (xs ys)
(declare (xargs :measure (+ (len xs) (len ys))))
(cond ((endp xs) ys)
((endp ys) xs)
((< (first xs) (first ys))
(cons (first xs) (mrg (rest xs) ys)))
(t (cons (first ys) (mrg xs (rest ys))))))
(defthm split-shortens
(implies (consp (rest xs))
(mv-let (ys zs)
(split xs)
(and (< (len ys) (len xs))
(< (len zs) (len xs))))))
(defun msort (xs)
(declare (xargs
:measure (len xs)
:hints (("Goal"
:use ((:instance split-shortens))))))
(if (endp (rest xs))
xs
(mv-let (ys zs)
(split xs)
(mrg (msort ys)
(msort zs)))))</lang>
ActionScript
<lang ActionScript>function mergesort(a:Array) { //Arrays of length 1 and 0 are always sorted if(a.length <= 1) return a; else { var middle:uint = a.length/2; //split the array into two var left:Array = new Array(middle); var right:Array = new Array(a.length-middle); var j:uint = 0, k:uint = 0; //fill the left array for(var i:uint = 0; i < middle; i++) left[j++]=a[i]; //fill the right array for(i = middle; i< a.length; i++) right[k++]=a[i]; //sort the arrays left = mergesort(left); right = mergesort(right); //If the last element of the left array is less than or equal to the first //element of the right array, they are in order and don't need to be merged if(left[left.length-1] <= right[0]) return left.concat(right); a = merge(left, right); return a; } }
function merge(left:Array, right:Array) { var result:Array = new Array(left.length + right.length); var j:uint = 0, k:uint = 0, m:uint = 0; //merge the arrays in order while(j < left.length && k < right.length) { if(left[j] <= right[k]) result[m++] = left[j++]; else result[m++] = right[k++]; } //If one of the arrays has remaining entries that haven't been merged, they //will be greater than the rest of the numbers merged so far, so put them on the //end of the array. for(; j < left.length; j++) result[m++] = left[j]; for(; k < right.length; k++) result[m++] = right[k]; return result; }</lang>
Ada
This example creates a generic package for sorting arrays of any type. Ada allows array indices to be any discrete type, including enumerated types which are non-numeric. Furthermore, numeric array indices can start at any value, positive, negative, or zero. The following code handles all the possible variations in index types. <lang ada>generic
type Element_Type is private; type Index_Type is (<>); type Collection_Type is array(Index_Type range <>) of Element_Type; with function "<"(Left, Right : Element_Type) return Boolean is <>;
package Mergesort is
function Sort(Item : Collection_Type) return Collection_Type;
end MergeSort;</lang>
<lang ada>package body Mergesort is
-----------
-- Merge --
-----------
function Merge(Left, Right : Collection_Type) return Collection_Type is
Result : Collection_Type(Left'First..Right'Last);
Left_Index : Index_Type := Left'First;
Right_Index : Index_Type := Right'First;
Result_Index : Index_Type := Result'First;
begin
while Left_Index <= Left'Last and Right_Index <= Right'Last loop
if Left(Left_Index) <= Right(Right_Index) then
Result(Result_Index) := Left(Left_Index);
Left_Index := Index_Type'Succ(Left_Index); -- increment Left_Index
else
Result(Result_Index) := Right(Right_Index);
Right_Index := Index_Type'Succ(Right_Index); -- increment Right_Index
end if;
Result_Index := Index_Type'Succ(Result_Index); -- increment Result_Index
end loop;
if Left_Index <= Left'Last then
Result(Result_Index..Result'Last) := Left(Left_Index..Left'Last);
end if;
if Right_Index <= Right'Last then
Result(Result_Index..Result'Last) := Right(Right_Index..Right'Last);
end if;
return Result;
end Merge;
----------
-- Sort --
----------
function Sort (Item : Collection_Type) return Collection_Type is
Result : Collection_Type(Item'range);
Middle : Index_Type;
begin
if Item'Length <= 1 then
return Item;
else
Middle := Index_Type'Val((Item'Length / 2) + Index_Type'Pos(Item'First));
declare
Left : Collection_Type(Item'First..Index_Type'Pred(Middle));
Right : Collection_Type(Middle..Item'Last);
begin
for I in Left'range loop
Left(I) := Item(I);
end loop;
for I in Right'range loop
Right(I) := Item(I);
end loop;
Left := Sort(Left);
Right := Sort(Right);
Result := Merge(Left, Right);
end;
return Result;
end if;
end Sort;
end Mergesort;</lang> The following code provides an usage example for the generic package defined above. <lang ada>with Ada.Text_Io; use Ada.Text_Io; with Mergesort;
procedure Mergesort_Test is
type List_Type is array(Positive range <>) of Integer;
package List_Sort is new Mergesort(Integer, Positive, List_Type);
procedure Print(Item : List_Type) is
begin
for I in Item'range loop
Put(Integer'Image(Item(I)));
end loop;
New_Line;
end Print;
List : List_Type := (1, 5, 2, 7, 3, 9, 4, 6);
begin
Print(List); Print(List_Sort.Sort(List));
end Mergesort_Test;</lang>
- Output:
1 5 2 7 3 9 4 6 1 2 3 4 5 6 7 9
ALGOL 68
Below are two variants of the same routine. If copying the DATA type to a different memory location is expensive, then the optimised version should be used as the DATA elements are handled indirectly. <lang algol68>MODE DATA = CHAR;
PROC merge sort = ([]DATA m)[]DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]DATA left = merge sort(m[:middle]);
[]DATA right = merge sort(m[middle+1:]);
flex merge(left, right)[AT LWB m]
FI
);
- FLEX version: A demonstration of FLEX for manipulating arrays #
PROC flex merge = ([]DATA in left, in right)[]DATA:(
[UPB in left + UPB in right]DATA result; FLEX[0]DATA left := in left; FLEX[0]DATA right := in right;
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF LWB right > UPB right THEN
result[index:] := left;
stop iteration
ELIF LWB left > UPB left THEN
result[index:] := right;
stop iteration
ELIF left[1] <= right[1] THEN
result[index] := left[1];
left := left[2:]
ELSE
result[index] := right[1];
right := right[2:]
FI
OD;
stop iteration:
result
);
[32]CHAR char array data := "big fjords vex quick waltz nymph"; print((merge sort(char array data), new line));</lang>
- Output:
abcdefghiijklmnopqrstuvwxyz
Optimised version:
- avoids FLEX array copies and manipulations
- avoids type DATA memory copies, useful in cases where DATA is a large STRUCT
<lang algol68>PROC opt merge sort = ([]REF DATA m)[]REF DATA: (
IF LWB m >= UPB m THEN
m
ELSE
INT middle = ( UPB m + LWB m ) OVER 2;
[]REF DATA left = opt merge sort(m[:middle]);
[]REF DATA right = opt merge sort(m[middle+1:]);
opt merge(left, right)[AT LWB m]
FI
);
PROC opt merge = ([]REF DATA left, right)[]REF DATA:(
[UPB left - LWB left + 1 + UPB right - LWB right + 1]REF DATA result; INT index left:=LWB left, index right:=LWB right;
FOR index TO UPB result DO
# change the direction of this comparison to change the direction of the sort #
IF index right > UPB right THEN
result[index:] := left[index left:];
stop iteration
ELIF index left > UPB left THEN
result[index:] := right[index right:];
stop iteration
ELIF left[index left] <= right[index right] THEN
result[index] := left[index left]; index left +:= 1
ELSE
result[index] := right[index right]; index right +:= 1
FI
OD;
stop iteration:
result
);
- create an array of pointers to the data being sorted #
[UPB char array data]REF DATA data; FOR i TO UPB char array data DO data[i] := char array data[i] OD;
[]REF CHAR result = opt merge sort(data); FOR i TO UPB result DO print((result[i])) OD; print(new line)</lang>
- Output:
abcdefghiijklmnopqrstuvwxyz
AutoHotkey_L
AutoHotkey_L has true array support and can dynamically grow and shrink its arrays at run time. This version of Merge Sort only needs n locations to sort. AHK forum post <lang AutoHotkey>#NoEnv
Test := [] Loop 100 {
Random n, 0, 999 Test.Insert(n)
} Result := MergeSort(Test) Loop % Result.MaxIndex() {
MsgBox, 1, , % Result[A_Index]
IfMsgBox Cancel
Break
} Return
/*
Function MergeSort
Sorts an array by first recursively splitting it down to its
individual elements and then merging those elements in their
correct order.
Parameters
Array The array to be sorted
Returns
The sorted array
- /
MergeSort(Array)
{
; Return single element arrays
If (! Array.HasKey(2))
Return Array
; Split array into Left and Right halfs
Left := [], Right := [], Middle := Array.MaxIndex() // 2
Loop % Middle
Right.Insert(Array.Remove(Middle-- + 1)), Left.Insert(Array.Remove(1))
If (Array.MaxIndex())
Right.Insert(Array.Remove(1))
Left := MergeSort(Left), Right := MergeSort(Right)
; If all the Right values are greater than all the
; Left values, just append Right at the end of Left.
If (Left[Left.MaxIndex()] <= Right[1]) {
Loop % Right.MaxIndex()
Left.Insert(Right.Remove(1))
Return Left
}
; Loop until one of the arrays is empty
While(Left.MaxIndex() and Right.MaxIndex())
Left[1] <= Right[1] ? Array.Insert(Left.Remove(1))
: Array.Insert(Right.Remove(1))
Loop % Left.MaxIndex()
Array.Insert(Left.Remove(1))
Loop % Right.MaxIndex()
Array.Insert(Right.Remove(1))
Return Array
}</lang>
AutoHotkey
Contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % MSort("") MsgBox % MSort("xxx") MsgBox % MSort("3,2,1") MsgBox % MSort("dog,000000,cat,pile,abcde,1,zz,xx,z")
MSort(x) { ; Merge-sort of a comma separated list
If (2 > L:=Len(x))
Return x ; empty or single item lists are sorted
StringGetPos p, x, `,, % "L" L//2 ; Find middle comma
Return Merge(MSort(SubStr(x,1,p)), MSort(SubStr(x,p+2))) ; Split, Sort, Merge
}
Len(list) {
StringReplace t, list,`,,,UseErrorLevel ; #commas -> ErrorLevel Return list="" ? 0 : ErrorLevel+1
}
Item(list,ByRef p) { ; item at position p, p <- next position
Return (p := InStr(list,",",0,i:=p+1)) ? SubStr(list,i,p-i) : SubStr(list,i)
}
Merge(list0,list1) { ; Merge 2 sorted lists
IfEqual list0,, Return list1
IfEqual list1,, Return list0
i0 := Item(list0,p0:=0)
i1 := Item(list1,p1:=0)
Loop {
i := i0>i1
list .= "," i%i% ; output smaller
If (p%i%)
i%i% := Item(list%i%,p%i%) ; get next item from processed list
Else {
i ^= 1 ; list is exhausted: attach rest of other
Return SubStr(list "," i%i% (p%i% ? "," SubStr(list%i%,p%i%+1) : ""), 2)
}
}
}</lang>
BBC BASIC
<lang BBCBASIC>DEFPROC_MergeSort(Start%,End%) REM ***************************************************************** REM This procedure Merge Sorts the chunk of data% bounded by REM Start% & End%. REM *****************************************************************
LOCAL Middle% IF End%=Start% ENDPROC
IF End%-Start%=1 THEN
IF data%(End%)<data%(Start%) THEN
SWAP data%(Start%),data%(End%)
ENDIF
ENDPROC
ENDIF
Middle%=Start%+(End%-Start%)/2
PROC_MergeSort(Start%,Middle%) PROC_MergeSort(Middle%+1,End%) PROC_Merge(Start%,Middle%,End%)
ENDPROC
DEF PROC_Merge(Start%,Middle%,End%)
LOCAL fh_size% fh_size% = Middle%-Start%+1
FOR I%=0 TO fh_size%-1
fh%(I%)=data%(Start%+I%)
NEXT I%
I%=0 J%=Middle%+1 K%=Start%
REPEAT
IF fh%(I%) <= data%(J%) THEN data%(K%)=fh%(I%) I%+=1 K%+=1 ELSE data%(K%)=data%(J%) J%+=1 K%+=1 ENDIF
UNTIL I%=fh_size% OR J%>End%
WHILE I% < fh_size%
data%(K%)=fh%(I%) I%+=1 K%+=1
ENDWHILE
ENDPROC</lang> Usage would look something like this example which sorts a series of 1000 random integers: <lang BBCBASIC>REM Example of merge sort usage. Size%=1000
S1%=Size%/2
DIM data%(Size%) DIM fh%(S1%)
FOR I%=1 TO Size%
data%(I%)=RND(100000)
NEXT
PROC_MergeSort(1,Size%)
END</lang>
C
<lang c>#include <stdio.h>
- include <stdlib.h>
void merge (int *a, int n, int m) {
int i, j, k;
int *x = malloc(n * sizeof (int));
for (i = 0, j = m, k = 0; k < n; k++) {
x[k] = j == n ? a[i++]
: i == m ? a[j++]
: a[j] < a[i] ? a[j++]
: a[i++];
}
for (i = 0; i < n; i++) {
a[i] = x[i];
}
free(x);
}
void merge_sort (int *a, int n) {
if (n < 2)
return;
int m = n / 2;
merge_sort(a, m);
merge_sort(a + m, n - m);
merge(a, n, m);
}
int main () {
int a[] = {4, 65, 2, -31, 0, 99, 2, 83, 782, 1};
int n = sizeof a / sizeof a[0];
int i;
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
merge_sort(a, n);
for (i = 0; i < n; i++)
printf("%d%s", a[i], i == n - 1 ? "\n" : " ");
return 0;
}</lang>
- Output:
4 65 2 -31 0 99 2 83 782 1 -31 0 1 2 2 4 65 83 99 782
C++
<lang cpp>#include <iterator>
- include <algorithm> // for std::inplace_merge
- include <functional> // for std::less
template<typename RandomAccessIterator, typename Order>
void mergesort(RandomAccessIterator first, RandomAccessIterator last, Order order)
{
if (last - first > 1)
{
RandomAccessIterator middle = first + (last - first) / 2;
mergesort(first, middle, order);
mergesort(middle, last, order);
std::inplace_merge(first, middle, last, order);
}
}
template<typename RandomAccessIterator>
void mergesort(RandomAccessIterator first, RandomAccessIterator last)
{
mergesort(first, last, std::less<typename std::iterator_traits<RandomAccessIterator>::value_type>());
}</lang>
C#
<lang csharp>namespace Sort {
using System;
public class MergeSort<T> where T : IComparable {
#region Constants
private const Int32 mergesDefault = 6;
private const Int32 insertionLimitDefault = 12;
#endregion
#region Properties
protected Int32[] Positions { get; set; }
private Int32 merges;
public Int32 Merges {
get { return merges; }
set {
// A minimum of 2 merges are required
if (value > 1)
merges = value;
else
throw new ArgumentOutOfRangeException();
if (Positions == null || Positions.Length != merges)
Positions = new Int32[merges];
}
}
public Int32 InsertionLimit { get; set; }
#endregion
#region Constructors
public MergeSort(Int32 merges, Int32 insertionLimit) {
Merges = merges;
InsertionLimit = insertionLimit;
}
public MergeSort()
: this(mergesDefault, insertionLimitDefault) {
}
#endregion
#region Sort Methods
public void Sort(T[] entries) {
// Allocate merge buffer
var entries2 = new T[entries.Length];
Sort(entries, entries2, 0, entries.Length - 1);
}
// Top-Down K-way Merge Sort
public void Sort(T[] entries1, T[] entries2, Int32 first, Int32 last) {
var length = last + 1 - first;
if (length < 2)
return;
else if (length < InsertionLimit) {
InsertionSort<T>.Sort(entries1, first, last);
return;
}
var left = first;
var size = ceiling(length, Merges);
for (var remaining = length; remaining > 0; remaining -= size, left += size) {
var right = left + Math.Min(remaining, size) - 1;
Sort(entries1, entries2, left, right);
}
Merge(entries1, entries2, first, last);
Array.Copy(entries2, first, entries1, first, length);
}
#endregion
#region Merge Methods
public void Merge(T[] entries1, T[] entries2, Int32 first, Int32 last) {
Array.Clear(Positions, 0, Merges);
// This implementation has a quadratic time dependency on the number of merges
for (var index = first; index <= last; index++)
entries2[index] = remove(entries1, first, last);
}
private T remove(T[] entries, Int32 first, Int32 last) {
var entry = default(T);
var found = (Int32?)null;
var length = last + 1 - first;
var index = 0;
var left = first;
var size = ceiling(length, Merges);
for (var remaining = length; remaining > 0; remaining -= size, left += size, index++) {
var position = Positions[index];
if (position < Math.Min(remaining, size)) {
var next = entries[left + position];
if (!found.HasValue || entry.CompareTo(next) > 0) {
found = index;
entry = next;
}
}
}
// Remove entry
Positions[found.Value]++;
return entry;
}
#endregion
#region Math Methods
private static Int32 ceiling(Int32 numerator, Int32 denominator) {
return (numerator + denominator - 1) / denominator;
}
#endregion
}
#region Insertion Sort
static class InsertionSort<T> where T : IComparable {
public static void Sort(T[] entries, Int32 first, Int32 last) {
for (var i = first + 1; i <= last; i++) {
var entry = entries[i];
var j = i;
while (j > first && entries[j - 1].CompareTo(entry) > 0)
entries[j] = entries[--j];
entries[j] = entry;
}
}
}
#endregion
}</lang> Example: <lang csharp> using Sort;
using System;
class Program {
static void Main(String[] args) {
var entries = new Int32[] { 7, 5, 2, 6, 1, 4, 2, 6, 3 };
var sorter = new MergeSort<Int32>();
sorter.Sort(entries);
Console.WriteLine(String.Join(" ", entries));
}
}</lang>
- Output:
1 2 2 3 4 5 6 6 7
Clojure
<lang lisp> (defn merge [left right]
(cond (nil? left) right
(nil? right) left
:else (let [[l & *left] left
[r & *right] right]
(if (<= l r) (cons l (merge *left right))
(cons r (merge left *right))))))
(defn merge-sort [list]
(if (< (count list) 2)
list
(let [[left right] (split-at (/ (count list) 2) list)]
(merge (merge-sort left) (merge-sort right)))))
</lang>
COBOL
Cobol cannot do recursion, so this version simulates recursion. The working storage is therefore pretty complex, so I have shown the whole program, not just the working procedure division parts. <lang COBOL> IDENTIFICATION DIVISION.
PROGRAM-ID. MERGESORT.
AUTHOR. DAVE STRATFORD.
DATE-WRITTEN. APRIL 2010.
INSTALLATION. HEXAGON SYSTEMS LIMITED.
******************************************************************
* MERGE SORT *
* The Merge sort uses a completely different paradigm, one of *
* divide and conquer, to many of the other sorts. The data set *
* is split into smaller sub sets upon which are sorted and then *
* merged together to form the final sorted data set. *
* This version uses the recursive method. Split the data set in *
* half and perform a merge sort on each half. This in turn splits*
* each half again and again until each set is just one or 2 items*
* long. A set of one item is already sorted so is ignored, a set *
* of two is compared and swapped as necessary. The smaller data *
* sets are then repeatedly merged together to eventually form the*
* full, sorted, set. *
* Since cobol cannot do recursion this module only simulates it *
* so is not as fast as a normal recursive version would be. *
* Scales very well to larger data sets, its relative complexity *
* means it is not suited to sorting smaller data sets: use an *
* Insertion sort instead as the Merge sort is a stable sort. *
******************************************************************
ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
SOURCE-COMPUTER. ICL VME.
OBJECT-COMPUTER. ICL VME.
INPUT-OUTPUT SECTION.
FILE-CONTROL.
SELECT FA-INPUT-FILE ASSIGN FL01.
SELECT FB-OUTPUT-FILE ASSIGN FL02.
DATA DIVISION.
FILE SECTION.
FD FA-INPUT-FILE.
01 FA-INPUT-REC.
03 FA-DATA PIC 9(6).
FD FB-OUTPUT-FILE.
01 FB-OUTPUT-REC PIC 9(6).
WORKING-STORAGE SECTION.
01 WA-IDENTITY.
03 WA-PROGNAME PIC X(10) VALUE "MERGESORT".
03 WA-VERSION PIC X(6) VALUE "000001".
01 WB-TABLE.
03 WB-ENTRY PIC 9(8) COMP SYNC OCCURS 100000
INDEXED BY WB-IX-1
WB-IX-2.
01 WC-VARS.
03 WC-SIZE PIC S9(8) COMP SYNC.
03 WC-TEMP PIC S9(8) COMP SYNC.
03 WC-START PIC S9(8) COMP SYNC.
03 WC-MIDDLE PIC S9(8) COMP SYNC.
03 WC-END PIC S9(8) COMP SYNC.
01 WD-FIRST-HALF.
03 WD-FH-MAX PIC S9(8) COMP SYNC.
03 WD-ENTRY PIC 9(8) COMP SYNC OCCURS 50000
INDEXED BY WD-IX.
01 WF-CONDITION-FLAGS.
03 WF-EOF-FLAG PIC X.
88 END-OF-FILE VALUE "Y".
03 WF-EMPTY-FILE-FLAG PIC X.
88 EMPTY-FILE VALUE "Y".
01 WS-STACK.
* This stack is big enough to sort a list of 1million items.
03 WS-STACK-ENTRY OCCURS 20 INDEXED BY WS-STACK-TOP.
05 WS-START PIC S9(8) COMP SYNC.
05 WS-MIDDLE PIC S9(8) COMP SYNC.
05 WS-END PIC S9(8) COMP SYNC.
05 WS-FS-FLAG PIC X.
88 FIRST-HALF VALUE "F".
88 SECOND-HALF VALUE "S".
88 WS-ALL VALUE "A".
05 WS-IO-FLAG PIC X.
88 WS-IN VALUE "I".
88 WS-OUT VALUE "O".
PROCEDURE DIVISION.
A-MAIN SECTION.
A-000.
PERFORM B-INITIALISE.
IF NOT EMPTY-FILE
PERFORM C-PROCESS.
PERFORM D-FINISH.
A-999.
STOP RUN.
B-INITIALISE SECTION.
B-000.
DISPLAY "*** " WA-PROGNAME " VERSION "
WA-VERSION " STARTING ***".
MOVE ALL "N" TO WF-CONDITION-FLAGS.
OPEN INPUT FA-INPUT-FILE.
SET WB-IX-1 TO 0.
READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG
WF-EMPTY-FILE-FLAG.
PERFORM BA-READ-INPUT UNTIL END-OF-FILE.
CLOSE FA-INPUT-FILE.
SET WC-SIZE TO WB-IX-1.
B-999.
EXIT.
BA-READ-INPUT SECTION.
BA-000.
SET WB-IX-1 UP BY 1.
MOVE FA-DATA TO WB-ENTRY(WB-IX-1).
READ FA-INPUT-FILE AT END MOVE "Y" TO WF-EOF-FLAG.
BA-999.
EXIT.
C-PROCESS SECTION.
C-000.
DISPLAY "SORT STARTING".
MOVE 1 TO WS-START(1).
MOVE WC-SIZE TO WS-END(1).
MOVE "F" TO WS-FS-FLAG(1).
MOVE "I" TO WS-IO-FLAG(1).
SET WS-STACK-TOP TO 2.
PERFORM E-MERGE-SORT UNTIL WS-OUT(1).
DISPLAY "SORT FINISHED".
C-999.
EXIT.
D-FINISH SECTION.
D-000.
OPEN OUTPUT FB-OUTPUT-FILE.
SET WB-IX-1 TO 1.
PERFORM DA-WRITE-OUTPUT UNTIL WB-IX-1 > WC-SIZE.
CLOSE FB-OUTPUT-FILE.
DISPLAY "*** " WA-PROGNAME " FINISHED ***".
D-999.
EXIT.
DA-WRITE-OUTPUT SECTION.
DA-000.
WRITE FB-OUTPUT-REC FROM WB-ENTRY(WB-IX-1).
SET WB-IX-1 UP BY 1.
DA-999.
EXIT.
******************************************************************
E-MERGE-SORT SECTION.
*===================== *
* This section controls the simulated recursion. *
******************************************************************
E-000.
IF WS-OUT(WS-STACK-TOP - 1)
GO TO E-010.
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
* First check size of part we are dealing with.
IF WC-END - WC-START = 0
* Only 1 number in range, so simply set for output, and move on
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
GO TO E-010.
IF WC-END - WC-START = 1
* 2 numbers, so compare and swap as necessary. Set for output
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1)
IF WB-ENTRY(WC-START) > WB-ENTRY(WC-END)
MOVE WB-ENTRY(WC-START) TO WC-TEMP
MOVE WB-ENTRY(WC-END) TO WB-ENTRY(WC-START)
MOVE WC-TEMP TO WB-ENTRY(WC-END)
GO TO E-010
ELSE
GO TO E-010.
* More than 2, so split and carry on down
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.
MOVE WC-START TO WS-START(WS-STACK-TOP).
MOVE WC-MIDDLE TO WS-END(WS-STACK-TOP).
MOVE "F" TO WS-FS-FLAG(WS-STACK-TOP).
MOVE "I" TO WS-IO-FLAG(WS-STACK-TOP).
SET WS-STACK-TOP UP BY 1.
GO TO E-999.
E-010.
SET WS-STACK-TOP DOWN BY 1.
IF SECOND-HALF(WS-STACK-TOP)
GO TO E-020.
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2 + 1.
MOVE WC-MIDDLE TO WS-START(WS-STACK-TOP).
MOVE WC-END TO WS-END(WS-STACK-TOP).
MOVE "S" TO WS-FS-FLAG(WS-STACK-TOP).
MOVE "I" TO WS-IO-FLAG(WS-STACK-TOP).
SET WS-STACK-TOP UP BY 1.
GO TO E-999.
E-020.
MOVE WS-START(WS-STACK-TOP - 1) TO WC-START.
MOVE WS-END(WS-STACK-TOP - 1) TO WC-END.
COMPUTE WC-MIDDLE = ( WC-START + WC-END ) / 2.
PERFORM H-PROCESS-MERGE.
MOVE "O" TO WS-IO-FLAG(WS-STACK-TOP - 1).
E-999.
EXIT.
******************************************************************
H-PROCESS-MERGE SECTION.
*======================== *
* This section identifies which data is to be merged, and then *
* merges the two data streams into a single larger data stream. *
******************************************************************
H-000.
INITIALISE WD-FIRST-HALF.
COMPUTE WD-FH-MAX = WC-MIDDLE - WC-START + 1.
SET WD-IX TO 1.
PERFORM HA-COPY-OUT VARYING WB-IX-1 FROM WC-START BY 1
UNTIL WB-IX-1 > WC-MIDDLE.
SET WB-IX-1 TO WC-START.
SET WB-IX-2 TO WC-MIDDLE.
SET WB-IX-2 UP BY 1.
SET WD-IX TO 1.
PERFORM HB-MERGE UNTIL WD-IX > WD-FH-MAX OR WB-IX-2 > WC-END.
PERFORM HC-COPY-BACK UNTIL WD-IX > WD-FH-MAX.
H-999.
EXIT.
HA-COPY-OUT SECTION.
HA-000.
MOVE WB-ENTRY(WB-IX-1) TO WD-ENTRY(WD-IX).
SET WD-IX UP BY 1.
HA-999.
EXIT.
HB-MERGE SECTION.
HB-000.
IF WB-ENTRY(WB-IX-2) < WD-ENTRY(WD-IX)
MOVE WB-ENTRY(WB-IX-2) TO WB-ENTRY(WB-IX-1)
SET WB-IX-2 UP BY 1
ELSE
MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1)
SET WD-IX UP BY 1.
SET WB-IX-1 UP BY 1.
HB-999.
EXIT.
HC-COPY-BACK SECTION.
HC-000.
MOVE WD-ENTRY(WD-IX) TO WB-ENTRY(WB-IX-1).
SET WD-IX UP BY 1.
SET WB-IX-1 UP BY 1.
HC-999.
EXIT.</lang>
CoffeeScript
<lang coffeescript># This is a simple version of mergesort that returns brand-new arrays.
- A more sophisticated version would do more in-place optimizations.
merge_sort = (arr) ->
if arr.length <= 1
return (elem for elem in arr)
m = Math.floor(arr.length / 2)
arr1 = merge_sort(arr.slice 0, m)
arr2 = merge_sort(arr.slice m)
result = []
p1 = p2 = 0
while true
if p1 >= arr1.length
if p2 >= arr2.length
return result
result.push arr2[p2]
p2 += 1
else if p2 >= arr2.length or arr1[p1] < arr2[p2]
result.push arr1[p1]
p1 += 1
else
result.push arr2[p2]
p2 += 1
do ->
console.log merge_sort [2,4,6,8,1,3,5,7,9,10,11,0,13,12]</lang>
- Output:
> coffee mergesort.coffee [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
Common Lisp
<lang lisp>(defun merge-sort (result-type sequence predicate)
(let ((split (floor (length sequence) 2)))
(if (zerop split)
(copy-seq sequence)
(merge result-type (merge-sort result-type (subseq sequence 0 split) predicate)
(merge-sort result-type (subseq sequence split) predicate)
predicate))))</lang>
merge is a standard Common Lisp function.
> (merge-sort 'list (list 1 3 5 7 9 8 6 4 2) #'<) (1 2 3 4 5 6 7 8 9)
Curry
Copied from Curry: Example Programs <lang curry>-- merge sort: sorting two lists by merging the sorted first -- and second half of the list
sort :: ([a] -> [a] -> [a] -> Success) -> [a] -> [a] -> Success
sort merge xs ys =
if length xs < 2 then ys =:= xs
else sort merge (firsthalf xs) us
& sort merge (secondhalf xs) vs
& merge us vs ys
where us,vs free
intMerge :: [Int] -> [Int] -> [Int] -> Success
intMerge [] ys zs = zs =:= ys intMerge (x:xs) [] zs = zs =:= x:xs intMerge (x:xs) (y:ys) zs =
if (x > y) then intMerge (x:xs) ys us & zs =:= y:us
else intMerge xs (y:ys) vs & zs =:= x:vs
where us,vs free
firsthalf xs = take (length xs `div` 2) xs secondhalf xs = drop (length xs `div` 2) xs
goal1 xs = sort intMerge [3,1,2] xs goal2 xs = sort intMerge [3,1,2,5,4,8] xs goal3 xs = sort intMerge [3,1,2,5,4,8,6,7,2,9,1,4,3] xs</lang>
D
Arrays only, not in-place. <lang d>import std.stdio, std.algorithm, std.array, std.range;
T[] mergeSorted(T)(in T[] D) /*pure nothrow @safe*/ {
if (D.length < 2)
return D.dup;
return [D[0 .. $ / 2].mergeSorted, D[$ / 2 .. $].mergeSorted]
.nWayUnion.array;
}
void main() {
[3, 4, 2, 5, 1, 6].mergeSorted.writeln;
}</lang>
Alternative Version
This in-place version allocates the auxiliary memory on the stack, making life easier for the garbage collector, but with risk of stack overflow (same output): <lang d>import std.stdio, std.algorithm, core.stdc.stdlib, std.exception,
std.range;
void mergeSort(T)(T[] data) if (hasSwappableElements!(typeof(data))) {
immutable L = data.length; if (L < 2) return; T* ptr = cast(T*)alloca(L * T.sizeof); enforce(ptr != null); ptr[0 .. L] = data[]; mergeSort(ptr[0 .. L/2]); mergeSort(ptr[L/2 .. L]); [ptr[0 .. L/2], ptr[L/2 .. L]].nWayUnion().copy(data);
}
void main() {
auto a = [3, 4, 2, 5, 1, 6]; a.mergeSort(); writeln(a);
}</lang>
Dart
<lang dart>merge(left, right, items) {
var a = 0;
var t;
while (left.length != 0 && right.length != 0) {
if (right[0] < left[0]) {
t = right[0];
right.removeRange(0,1);
} else {
t = left[0];
left.removeRange(0,1);
}
items[a++] = t;
}
while(left.length != 0) {
t = left[0];
left.removeRange(0,1);
items[a++] = t;
}
while(right.length != 0) {
t = right[0];
right.removeRange(0,1);
items[a++] = t;
}
}
mSort(items, tmp, l) {
if (l == 1) {
return;
}
var m = (l/2).floor().toInt();
var tmp_l = tmp.getRange(0, m);
var tmp_r = tmp.getRange(m, tmp.length-m);
mSort(tmp_l, items.getRange(0,m), m);
mSort(tmp_r, items.getRange(m, items.length-m), l-m);
merge(tmp_l, tmp_r, items);
}
merge_sort(items) {
mSort(items,items.getRange(0, items.length),items.length);
}
void main() {
var arr=[1,5,2,7,3,9,4,6,8];
print("Before sort");
arr.forEach((var i)=>print("$i"));
merge_sort(arr);
print("After sort");
arr.forEach((var i)=>print("$i"));
}</lang>
E
<lang e>def merge(var xs :List, var ys :List) {
var result := []
while (xs =~ [x] + xr && ys =~ [y] + yr) {
if (x <= y) {
result with= x
xs := xr
} else {
result with= y
ys := yr
}
}
return result + xs + ys
}
def sort(list :List) {
if (list.size() <= 1) { return list }
def split := list.size() // 2
return merge(sort(list.run(0, split)),
sort(list.run(split)))
}</lang>
Eiffel
<lang Eiffel> class MERGE_SORT [G -> COMPARABLE]
create sort
feature
sort (ar: ARRAY [G]) -- Sorted array in ascending order. require ar_not_empty: not ar.is_empty do create sorted_array.make_empty mergesort (ar, 1, ar.count) sorted_array := ar ensure sorted_array_not_empty: not sorted_array.is_empty sorted: is_sorted (sorted_array, 1, sorted_array.count) end
sorted_array: ARRAY [G]
feature {NONE}
mergesort (ar: ARRAY [G]; l, r: INTEGER) -- Sorting part of mergesort. local m: INTEGER do if l < r then m := (l + r) // 2 mergesort (ar, l, m) mergesort (ar, m + 1, r) merge (ar, l, m, r) end end
merge (ar: ARRAY [G]; l, m, r: INTEGER) -- Merge part of mergesort. require positive_index_l: l >= 1 positive_index_m: m >= 1 positive_index_r: r >= 1 ar_not_empty: not ar.is_empty local merged: ARRAY [G] h, i, j, k: INTEGER do i := l j := m + 1 k := l create merged.make_filled (ar [1], 1, ar.count) from until i > m or j > r loop if ar.item (i) <= ar.item (j) then merged.force (ar.item (i), k) i := i + 1 elseif ar.item (i) > ar.item (j) then merged.force (ar.item (j), k) j := j + 1 end k := k + 1 end if i > m then from h := j until h > r loop merged.force (ar.item (h), k + h - j) h := h + 1 end elseif j > m then from h := i until h > m loop merged.force (ar.item (h), k + h - i) h := h + 1 end end from h := l until h > r loop ar.item (h) := merged.item (h) h := h + 1 end ensure is_partially_sorted: is_sorted (ar, l, r) end
is_sorted (ar: ARRAY [G]; l, r: INTEGER): BOOLEAN -- Is 'ar' sorted in ascending order? require ar_not_empty: not ar.is_empty l_in_range: l >= 1 r_in_range: r <= ar.count local i: INTEGER do Result := True from i := l until i = r loop if ar [i] > ar [i + 1] then Result := False end i := i + 1 end end
end </lang> Test: <lang Eiffel> class APPLICATION
create make
feature
make do test := <<2, 5, 66, -2, 0, 7>> io.put_string ("unsorted" + "%N") across test as ar loop io.put_string (ar.item.out + "%T") end io.put_string ("%N" + "sorted" + "%N") create merge.sort (test) across merge.sorted_array as ar loop io.put_string (ar.item.out + "%T") end end
test: ARRAY [INTEGER]
merge: MERGE_SORT [INTEGER]
end </lang>
- Output:
unsorted 2 5 66 -2 0 7 sorted -2 0 2 5 7 66
Elixir
<lang elixir>defmodule Sort do
def merge_sort(list) when length(list) <= 1, do: list
def merge_sort(list) do
{left, right} = Enum.split(list, div(length(list), 2))
:lists.merge( merge_sort(left), merge_sort(right))
end
end</lang> Example:
iex(10)> Sort.merge_sort([5,3,9,4,1,6,8,2,7]) [1, 2, 3, 4, 5, 6, 7, 8, 9]
Erlang
Below are two versions. Both take advantage of built-in Erlang functions, lists:split and list:merge. The multi-process version spawns a new process each time it splits. This was slightly faster on a test system with only two cores, so it may not be the best implementation, however it does illustrate how easy it can be to add multi-threaded/process capabilities to a program.
Single-threaded version: <lang erlang>mergeSort(L) when length(L) == 1 -> L; mergeSort(L) when length(L) > 1 ->
{L1, L2} = lists:split(length(L) div 2, L),
lists:merge(mergeSort(L1), mergeSort(L2)).</lang>
Multi-process version: <lang erlang>pMergeSort(L) when length(L) == 1 -> L; pMergeSort(L) when length(L) > 1 ->
{L1, L2} = lists:split(length(L) div 2, L),
spawn(mergesort, pMergeSort2, [L1, self()]),
spawn(mergesort, pMergeSort2, [L2, self()]),
mergeResults([]).
pMergeSort2(L, Parent) when length(L) == 1 -> Parent ! L; pMergeSort2(L, Parent) when length(L) > 1 ->
{L1, L2} = lists:split(length(L) div 2, L),
spawn(mergesort, pMergeSort2, [L1, self()]),
spawn(mergesort, pMergeSort2, [L2, self()]),
Parent ! mergeResults([]).</lang>
ERRE
<lang ERRE> PROGRAM MERGESORT_DEMO
! Example of merge sort usage.
CONST SIZE%=100,S1%=50
DIM DTA%[SIZE%],FH%[S1%],STACK%[20,2]
PROCEDURE MERGE(START%,MIDDLE%,ENDS%)
LOCAL FHSIZE%
FHSIZE%=MIDDLE%-START%+1
FOR I%=0 TO FHSIZE%-1 DO
FH%[I%]=DTA%[START%+I%]
END FOR
I%=0 J%=MIDDLE%+1 K%=START%
REPEAT
IF FH%[I%]<=DTA%[J%] THEN
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
ELSE
DTA%[K%]=DTA%[J%]
J%=J%+1
K%=K%+1
END IF
UNTIL I%=FHSIZE% OR J%>ENDS%
WHILE I%<FHSIZE% DO
DTA%[K%]=FH%[I%]
I%=I%+1
K%=K%+1
END WHILE
END PROCEDURE
PROCEDURE MERGE_SORT(LEV->LEV)
! ***************************************************************** ! This procedure Merge Sorts the chunk of DTA% bounded by ! Start% & Ends%. ! *****************************************************************
LOCAL MIDDLE%
IF ENDS%=START% THEN LEV=LEV-1 EXIT PROCEDURE END IF
IF ENDS%-START%=1 THEN
IF DTA%[ENDS%]<DTA%[START%] THEN
SWAP(DTA%[START%],DTA%[ENDS%])
END IF
LEV=LEV-1
EXIT PROCEDURE
END IF
MIDDLE%=START%+(ENDS%-START%)/2
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE% START%=START% ENDS%=MIDDLE% MERGE_SORT(LEV+1->LEV) START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
STACK%[LEV,0]=START% STACK%[LEV,1]=ENDS% STACK%[LEV,2]=MIDDLE% START%=MIDDLE%+1 ENDS%=ENDS% MERGE_SORT(LEV+1->LEV) START%=STACK%[LEV,0] ENDS%=STACK%[LEV,1] MIDDLE%=STACK%[LEV,2]
MERGE(START%,MIDDLE%,ENDS%)
LEV=LEV-1
END PROCEDURE
BEGIN
FOR I%=1 TO SIZE% DO
DTA%[I%]=RND(1)*10000
END FOR
START%=1 ENDS%=SIZE% MERGE_SORT(0->LEV)
FOR I%=1 TO SIZE% DO
WRITE("#####";DTA%[I%];)
END FOR
PRINT
END PROGRAM </lang>
Euphoria
<lang euphoria>function merge(sequence left, sequence right)
sequence result
result = {}
while length(left) > 0 and length(right) > 0 do
if compare(left[1], right[1]) <= 0 then
result = append(result, left[1])
left = left[2..$]
else
result = append(result, right[1])
right = right[2..$]
end if
end while
return result & left & right
end function
function mergesort(sequence m)
sequence left, right
integer middle
if length(m) <= 1 then
return m
else
middle = floor(length(m)/2)
left = mergesort(m[1..middle])
right = mergesort(m[middle+1..$])
if compare(left[$], right[1]) <= 0 then
return left & right
elsif compare(right[$], left[1]) <= 0 then
return right & left
else
return merge(left, right)
end if
end if
end function
constant s = rand(repeat(1000,10)) ? s ? mergesort(s)</lang>
- Output:
{385,599,284,650,457,804,724,300,434,722}
{284,300,385,434,457,599,650,722,724,804}
F#
<lang fsharp>let split list =
let rec aux l acc1 acc2 =
match l with
| [] -> (acc1,acc2)
| [x] -> (x::acc1,acc2)
| x::y::tail ->
aux tail (x::acc1) (y::acc2)
in aux list [] []
let rec merge l1 l2 =
match (l1,l2) with
| (x,[]) -> x
| ([],y) -> y
| (x::tx,y::ty) ->
if x <= y then x::merge tx l2
else y::merge l1 ty
let rec mergesort list =
match list with
| [] -> []
| [x] -> [x]
| _ -> let (l1,l2) = split list
in merge (mergesort l1) (mergesort l2)</lang>
Factor
<lang factor>: mergestep ( accum seq1 seq2 -- accum seq1 seq2 ) 2dup [ first ] bi@ < [ [ [ first ] [ rest-slice ] bi [ suffix ] dip ] dip ] [ [ first ] [ rest-slice ] bi [ swap [ suffix ] dip ] dip ] if ;
- merge ( seq1 seq2 -- merged )
[ { } ] 2dip [ 2dup [ length 0 > ] bi@ and ] [ mergestep ] while append append ;
- mergesort ( seq -- sorted )
dup length 1 > [ dup length 2 / floor [ head ] [ tail ] 2bi [ mergesort ] bi@ merge ] [ ] if ;</lang>
<lang factor>( scratchpad ) { 4 2 6 5 7 1 3 } mergesort . { 1 2 3 4 5 6 7 }</lang>
Forth
This is an in-place mergesort which works on arrays of integers. <lang forth>: merge-step ( right mid left -- right mid+ left+ )
over @ over @ < if over @ >r 2dup - over dup cell+ rot move r> over ! >r cell+ 2dup = if rdrop dup else r> then then cell+ ;
- merge ( right mid left -- right left )
dup >r begin 2dup > while merge-step repeat 2drop r> ;
- mid ( l r -- mid ) over - 2/ cell negate and + ;
- mergesort ( right left -- right left )
2dup cell+ <= if exit then swap 2dup mid recurse rot recurse merge ;
- sort ( addr len -- ) cells over + swap mergesort 2drop ;
create test 8 , 1 , 5 , 3 , 9 , 0 , 2 , 7 , 6 , 4 ,
- .array ( addr len -- ) 0 do dup i cells + @ . loop drop ;
test 10 2dup sort .array \ 0 1 2 3 4 5 6 7 8 9</lang>
Fortran
<lang fortran>subroutine Merge(A,NA,B,NB,C,NC)
integer, intent(in) :: NA,NB,NC ! Normal usage: NA+NB = NC
integer, intent(in out) :: A(NA) ! B overlays C(NA+1:NC)
integer, intent(in) :: B(NB)
integer, intent(in out) :: C(NC)
integer :: I,J,K
I = 1; J = 1; K = 1;
do while(I <= NA .and. J <= NB)
if (A(I) <= B(J)) then
C(K) = A(I)
I = I+1
else
C(K) = B(J)
J = J+1
endif
K = K + 1
enddo
do while (I <= NA)
C(K) = A(I)
I = I + 1
K = K + 1
enddo
return
end subroutine merge
recursive subroutine MergeSort(A,N,T)
integer, intent(in) :: N
integer, dimension(N), intent(in out) :: A
integer, dimension((N+1)/2), intent (out) :: T
integer :: NA,NB,V
if (N < 2) return
if (N == 2) then
if (A(1) > A(2)) then
V = A(1)
A(1) = A(2)
A(2) = V
endif
return
endif
NA=(N+1)/2
NB=N-NA
call MergeSort(A,NA,T) call MergeSort(A(NA+1),NB,T)
if (A(NA) > A(NA+1)) then
T(1:NA)=A(1:NA)
call Merge(T,NA,A(NA+1),NB,A,N)
endif
return
end subroutine MergeSort
program TestMergeSort
integer, parameter :: N = 8 integer, dimension(N) :: A = (/ 1, 5, 2, 7, 3, 9, 4, 6 /) integer, dimension ((N+1)/2) :: T call MergeSort(A,N,T) write(*,'(A,/,10I3)')'Sorted array :',A
end program TestMergeSort</lang>
FunL
<lang funl>def
sort( [] ) = [] sort( [x] ) = [x] sort( xs ) = val (l, r) = xs.splitAt( xs.length()\2 ) merge( sort(l), sort(r) )
merge( [], xs ) = xs merge( xs, [] ) = xs merge( x:xs, y:ys ) | x <= y = x : merge( xs, y:ys ) | otherwise = y : merge( x:xs, ys )
println( sort([94, 37, 16, 56, 72, 48, 17, 27, 58, 67]) ) println( sort(['Sofía', 'Alysha', 'Sophia', 'Maya', 'Emma', 'Olivia', 'Emily']) )</lang>
- Output:
[16, 17, 27, 37, 48, 56, 58, 67, 72, 94] [Alysha, Emily, Emma, Maya, Olivia, Sofía, Sophia]
Go
<lang go>package main
import "fmt"
var a = []int{170, 45, 75, -90, -802, 24, 2, 66} var s = make([]int, len(a)/2+1) // scratch space for merge step
func main() {
fmt.Println("before:", a)
mergeSort(a)
fmt.Println("after: ", a)
}
func mergeSort(a []int) {
if len(a) < 2 {
return
}
mid := len(a) / 2
mergeSort(a[:mid])
mergeSort(a[mid:])
if a[mid-1] <= a[mid] {
return
}
// merge step, with the copy-half optimization
copy(s, a[:mid])
l, r := 0, mid
for i := 0; ; i++ {
if s[l] <= a[r] {
a[i] = s[l]
l++
if l == mid {
break
}
} else {
a[i] = a[r]
r++
if r == len(a) {
copy(a[i+1:], s[l:mid])
break
}
}
}
return
}</lang>
Groovy
This is the standard algorithm, except that in the looping phase of the merge we work backwards through the left and right lists to construct the merged list, to take advantage of the Groovy List.pop() method. However, this results in a partially merged list in reverse sort order; so we then reverse it to put in back into correct order. This could play havoc with the sort stability, but we compensate by picking aggressively from the right list (ties go to the right), rather than aggressively from the left as is done in the standard algorithm. <lang groovy>def merge = { List left, List right ->
List mergeList = []
while (left && right) {
print "."
mergeList << ((left[-1] > right[-1]) ? left.pop() : right.pop())
}
mergeList = mergeList.reverse()
mergeList = left + right + mergeList
}
def mergeSort; mergeSort = { List list ->
def n = list.size() if (n < 2) return list def middle = n.intdiv(2) def left = [] + list[0..<middle] def right = [] + list[middle..<n] left = mergeSort(left) right = mergeSort(right) if (left[-1] <= right[0]) return left + right merge(left, right)
}</lang> Test: <lang groovy>println (mergeSort([23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4])) println (mergeSort([88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1])) println () println (mergeSort([10, 10.0, 10.00, 1])) println (mergeSort([10, 10.00, 10.0, 1])) println (mergeSort([10.0, 10, 10.00, 1])) println (mergeSort([10.0, 10.00, 10, 1])) println (mergeSort([10.00, 10, 10.0, 1])) println (mergeSort([10.00, 10.0, 10, 1]))</lang> The presence of decimal and integer versions of the same numbers, demonstrates, but of course does not prove, that the sort remains stable.
- Output:
.............................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99] ....................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88] ....[1, 10, 10.0, 10.00] ....[1, 10, 10.00, 10.0] ....[1, 10.0, 10, 10.00] ....[1, 10.0, 10.00, 10] ....[1, 10.00, 10, 10.0] ....[1, 10.00, 10.0, 10]
Tail recursion version
It is possible to write a version based on tail recursion, similar to that written in Haskel, OCaml or F#. This version also takes into account stack overflow problems induced by recursion for large lists using closure trampolines: <lang groovy>split = { list ->
list.collate((list.size()+1)/2 as int)
}
merge = { left, right, headBuffer=[] ->
if(left.size() == 0) headBuffer+right else if(right.size() == 0) headBuffer+left else if(left.head() <= right.head()) merge.trampoline(left.tail(), right, headBuffer+left.head()) else merge.trampoline(right.tail(), left, headBuffer+right.head())
}.trampoline()
mergesort = { List list ->
if(list.size() < 2) list
else merge(split(list).collect {mergesort it})
}
assert mergesort((500..1)) == (1..500) assert mergesort([5,4,6,3,1,2]) == [1,2,3,4,5,6] assert mergesort([3,3,1,4,6,78,9,1,3,5]) == [1,1,3,3,3,4,5,6,9,78] </lang>
which uses List.collate(), alternatively one could write a purely recursive split() closure as:
<lang groovy>
split = { list, left=[], right=[] ->
if(list.size() <2) [list+left, right] else split.trampoline(list.tail().tail(), [list.head()]+left,[list.tail().head()]+right)
}.trampoline() </lang>
Haskell
Splitting in half in the middle like the normal merge sort does would be inefficient on the singly-linked lists used in Haskell (since you would have to do one pass just to determine the length, and then another half-pass to do the splitting). Instead, the algorithm here splits the list in half in a different way -- by alternately assigning elements to one list and the other. That way we (lazily) construct both sublists in parallel as we traverse the original list. Unfortunately, under this way of splitting we cannot do a stable sort. <lang haskell>merge [] ys = ys merge xs [] = xs merge xs@(x:xt) ys@(y:yt) | x <= y = x : merge xt ys
| otherwise = y : merge xs yt
split (x:y:zs) = let (xs,ys) = split zs in (x:xs,y:ys) split [x] = ([x],[]) split [] = ([],[])
mergeSort [] = [] mergeSort [x] = [x] mergeSort xs = let (as,bs) = split xs
in merge (mergeSort as) (mergeSort bs)</lang>
Alternatively, we can use bottom-up mergesort. This starts with lots of tiny sorted lists, and repeatedly merges pairs of them, building a larger and larger sorted list <lang haskell>mergePairs (sorted1 : sorted2 : sorteds) = merge sorted1 sorted2 : mergePairs sorteds mergePairs sorteds = sorteds
mergeSortBottomUp list = mergeAll (map (\x -> [x]) list)
mergeAll [sorted] = sorted mergeAll sorteds = mergeAll (mergePairs sorteds)</lang> The standard library's sort function in GHC takes a similar approach to the bottom-up code, the differece being that, instead of starting with lists of size one, which are sorted by default, it detects runs in original list and uses those: <lang haskell>sort = sortBy compare sortBy cmp = mergeAll . sequences
where
sequences (a:b:xs)
| a `cmp` b == GT = descending b [a] xs
| otherwise = ascending b (a:) xs
sequences xs = [xs]
descending a as (b:bs)
| a `cmp` b == GT = descending b (a:as) bs
descending a as bs = (a:as): sequences bs
ascending a as (b:bs)
| a `cmp` b /= GT = ascending b (\ys -> as (a:ys)) bs
ascending a as bs = as [a]: sequences bs</lang>
In this code, mergeAll, mergePairs, and merge are as above, except using the specialized cmp function in merge.
Io
<lang io>List do (
merge := method(lst1, lst2,
result := list()
while(lst1 isNotEmpty or lst2 isNotEmpty,
if(lst1 first <= lst2 first) then(
result append(lst1 removeFirst)
) else (
result append(lst2 removeFirst)
)
)
result)
mergeSort := method(
if (size > 1) then(
half_size := (size / 2) ceil
return merge(slice(0, half_size) mergeSort,
slice(half_size, size) mergeSort)
) else (return self)
)
mergeSortInPlace := method(
copy(mergeSort)
)
)
lst := list(9, 5, 3, -1, 15, -2) lst mergeSort println # ==> list(-2, -1, 3, 5, 9, 15) lst mergeSortInPlace println # ==> list(-2, -1, 3, 5, 9, 15)</lang>
Icon and Unicon
<lang Icon>procedure main() #: demonstrate various ways to sort a list and string
demosort(mergesort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
end
procedure mergesort(X,op,lower,upper) #: return sorted list ascending(or descending) local middle
if /lower := 1 then { # top level call setup
upper := *X
op := sortop(op,X) # select how and what we sort
}
if upper ~= lower then { # sort all sections with 2 or more elements
X := mergesort(X,op,lower,middle := lower + (upper - lower) / 2)
X := mergesort(X,op,middle+1,upper)
if op(X[middle+1],X[middle]) then # @middle+1 < @middle merge if halves reversed
X := merge(X,op,lower,middle,upper)
}
return X
end
procedure merge(X,op,lower,middle,upper) # merge two list sections within a larger list local p1,p2,add
p1 := lower
p2 := middle + 1
add := if type(X) ~== "string" then put else "||" # extend X, strings require X := add (until ||:= is invocable)
while p1 <= middle & p2 <= upper do
if op(X[p1],X[p2]) then { # @p1 < @p2
X := add(X,X[p1]) # extend X temporarily (rather than use a separate temporary list)
p1 +:= 1
}
else {
X := add(X,X[p2]) # extend X temporarily
p2 +:= 1
}
while X := add(X,X[middle >= p1]) do p1 +:= 1 # and rest of lower or ...
while X := add(X,X[upper >= p2]) do p2 +:= 1 # ... upper trailers if any
if type(X) ~== "string" then # pull section's sorted elements from extension
every X[upper to lower by -1] := pull(X)
else
(X[lower+:(upper-lower+1)] := X[0-:(upper-lower+1)])[0-:(upper-lower+1)] := ""
return X
end</lang>
Note: This example relies on the supporting procedures 'sortop', and 'demosort' in Bubble Sort. The full demosort exercises the named sort of a list with op = "numeric", "string", ">>" (lexically gt, descending),">" (numerically gt, descending), a custom comparator, and also a string.
- Output:
Abbreviated sample
Sorting Demo using procedure mergesort
on list : [ 3 14 1 5 9 2 6 3 ]
with op = &null: [ 1 2 3 3 5 6 9 14 ] (0 ms)
...
on string : "qwerty"
with op = &null: "eqrtwy" (0 ms)
J
Solution <lang j>merge =: ,`(({.@] , ($: }.))~` ({.@] , ($: }.)) @.(>&{.))@.(*@*&#) split =: </.~ 0 1$~# mergeSort =: merge & $: &>/ @ split ` ] @. (1>:#)</lang> This version is usable for relative small arrays due to stack limitations for the recursive verb 'merge'. For larger arrays replace 'merge' with the following explicit non-recursive version: <lang j>merge=: 4 : 0
if. 0= x *@*&# y do. x,y return. end.
la=.x
ra=.y
z=.i.0
while. la *@*&# ra do.
if. la >&{. ra do.
z=.z,{.ra
ra=.}.ra
else.
z=.z,{.la
la=.}.la
end.
end.
z,la,ra
)</lang> But don't forget to use J's primitives /: or \: if you really need a sort-function.
Java
<lang java5>import java.util.List; import java.util.ArrayList; import java.util.Iterator;
public class Merge{
public static <E extends Comparable<? super E>> List<E> mergeSort(List<E> m){
if(m.size() <= 1) return m;
int middle = m.size() / 2;
List<E> left = m.subList(0, middle);
List<E> right = m.subList(middle, m.size());
right = mergeSort(right);
left = mergeSort(left);
List<E> result = merge(left, right);
return result; }
public static <E extends Comparable<? super E>> List<E> merge(List<E> left, List<E> right){
List<E> result = new ArrayList<E>();
Iterator<E> it1 = left.iterator();
Iterator<E> it2 = right.iterator();
E x = it1.next(); E y = it2.next();
while (true){
//change the direction of this comparison to change the direction of the sort
if(x.compareTo(y) <= 0){
result.add(x); if(it1.hasNext()){ x = it1.next(); }else{ result.add(y); while(it2.hasNext()){ result.add(it2.next()); } break; } }else{ result.add(y); if(it2.hasNext()){ y = it2.next(); }else{ result.add(x); while (it1.hasNext()){ result.add(it1.next()); } break; } }
}
return result;
}
}</lang>
JavaScript
<lang javascript>function merge(left, right, arr) {
var a = 0;
while (left.length && right.length) {
arr[a++] = (right[0] < left[0]) ? right.shift() : left.shift();
}
while (left.length) {
arr[a++] = left.shift();
}
while (right.length) {
arr[a++] = right.shift();
}
}
function mSort(arr, tmp, len) {
if (len === 1) { return; }
var m = Math.floor(len / 2),
tmp_l = tmp.slice(0, m),
tmp_r = tmp.slice(m);
mSort(tmp_l, arr.slice(0, m), m); mSort(tmp_r, arr.slice(m), len - m); merge(tmp_l, tmp_r, arr);
}
function merge_sort(arr) {
mSort(arr, arr.slice(), arr.length);
}
var arr = [1, 5, 2, 7, 3, 9, 4, 6, 8]; merge_sort(arr); // arr will now: 1, 2, 3, 4, 5, 6, 7, 8, 9</lang>
jq
The sort function defined here will sort any JSON array. <lang jq># Input: [x,y] -- the two arrays to be merged
- If x and y are sorted as by "sort", then the result will also be sorted:
def merge:
def m: # state: [x, y, array] (array being the answer)
.[0] as $x
| .[1] as $y
| if 0 == ($x|length) then .[2] + $y
elif 0 == ($y|length) then .[2] + $x
else
(if $x[0] <= $y[0] then [$x[1:], $y, .[2] + [$x[0] ]]
else [$x, $y[1:], .[2] + [$y[0] ]]
end) | m
end;
[.[0], .[1], []] | m;
def merge_sort:
if length <= 1 then . else (length/2 |floor) as $len | . as $in | [ ($in[0:$len] | merge_sort), ($in[$len:] | merge_sort) ] | merge end;</lang>
Example: <lang jq> ( [1, 3, 8, 9, 0, 0, 8, 7, 1, 6],
[170, 45, 75, 90, 2, 24, 802, 66], [170, 45, 75, 90, 2, 24, -802, -66] )
| (merge_sort == sort)</lang>
- Output:
true true true
Julia
<lang Julia>function mergesort!(A::AbstractVector)
if length(A) <= 1
return A
end
middle = div(length(A), 2)
left = mergesort(A[1:middle])
right = mergesort(A[middle + 1:end])
result = Array(eltype(left), length(left) + length(right))
idx = 1
@inbounds while !isempty(left) && !isempty(right)
if left[1] <= right[1]
result[idx] = left[1]
left = left[2:end]
else
result[idx] = right[1]
right = right[2:end]
end
idx += 1
end
@inbounds while !isempty(left)
result[idx] = left[1]
left = left[2:end]
idx += 1
end
@inbounds while !isempty(right)
result[idx] = right[1]
right = right[2:end]
idx += 1
end
for i=1:length(A)
A[i] = result[i]
end
return A
end
function mergesort(A::AbstractVector)
return mergesort!(copy(A))
end
A = randcycle(10) println("unsorted: ", A) println("sorted: ", mergesort(A))</lang>
- Output:
unsorted: [5,4,8,7,6,3,1,10,2,9] sorted: [1,2,3,4,5,6,7,8,9,10]
Kotlin
<lang kotlin>fun mergeSort(list: List<Int>): List<Int> {
if (list.size <= 1) {
return list
}
val left = mutableListOf<Int>() val right = mutableListOf<Int>()
val middle = list.size / 2
list.forEachIndexed { index, number ->
if (index < middle) {
left.add(number)
} else {
right.add(number)
}
}
fun merge(left: List<Int>, right: List<Int>): List<Int> = mutableListOf<Int>().apply {
var indexLeft = 0
var indexRight = 0
while (indexLeft < left.size && indexRight < right.size) {
if (left[indexLeft] <= right[indexRight]) {
add(left[indexLeft])
indexLeft++
} else {
add(right[indexRight])
indexRight++
}
}
while (indexLeft < left.size) {
add(left[indexLeft])
indexLeft++
}
while (indexRight < right.size) {
add(right[indexRight])
indexRight++
}
}
return merge(mergeSort(left), mergeSort(right))
}
fun main(args: Array<String>) {
val numbers = listOf(5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7)
println("Unsorted: $numbers")
println("Sorted: ${mergeSort(numbers)}")
}</lang>
- Output:
Unsorted: [5, 2, 3, 17, 12, 1, 8, 3, 4, 9, 7] Sorted: [1, 2, 3, 3, 4, 5, 7, 8, 9, 12, 17]
Liberty BASIC
<lang lb> itemCount = 20
dim A(itemCount) dim tmp(itemCount) 'merge sort needs additionally same amount of storage
for i = 1 to itemCount
A(i) = int(rnd(1) * 100)
next i
print "Before Sort" call printArray itemCount
call mergeSort 1,itemCount
print "After Sort" call printArray itemCount
end
'------------------------------------------ sub mergeSort start, theEnd
if theEnd-start < 1 then exit sub
if theEnd-start = 1 then
if A(start)>A(theEnd) then
tmp=A(start)
A(start)=A(theEnd)
A(theEnd)=tmp
end if
exit sub
end if
middle = int((start+theEnd)/2)
call mergeSort start, middle
call mergeSort middle+1, theEnd
call merge start, middle, theEnd
end sub
sub merge start, middle, theEnd
i = start: j = middle+1: k = start
while i<=middle OR j<=theEnd
select case
case i<=middle AND j<=theEnd
if A(i)<=A(j) then
tmp(k)=A(i)
i=i+1
else
tmp(k)=A(j)
j=j+1
end if
k=k+1
case i<=middle
tmp(k)=A(i)
i=i+1
k=k+1
case else 'j<=theEnd
tmp(k)=A(j)
j=j+1
k=k+1
end select
wend
for i = start to theEnd
A(i)=tmp(i)
next
end sub
'=========================================== sub printArray itemCount
for i = 1 to itemCount
print using("###", A(i));
next i
print
end sub</lang>
Logo
<lang logo>to split :size :front :list
if :size < 1 [output list :front :list] output split :size-1 (lput first :list :front) (butfirst :list)
end
to merge :small :large
if empty? :small [output :large] ifelse lessequal? first :small first :large ~ [output fput first :small merge butfirst :small :large] ~ [output fput first :large merge butfirst :large :small]
end
to mergesort :list
localmake "half split (count :list) / 2 [] :list if empty? first :half [output :list] output merge mergesort first :half mergesort last :half
end</lang>
Logtalk
<lang logtalk>msort([], []) :- !. msort([X], [X]) :- !. msort([X, Y| Xs], Ys) :-
split([X, Y| Xs], X1s, X2s), msort(X1s, Y1s), msort(X2s, Y2s), merge(Y1s, Y2s, Ys).
split([], [], []). split([X| Xs], [X| Ys], Zs) :-
split(Xs, Zs, Ys).
merge([X| Xs], [Y| Ys], [X| Zs]) :-
X @=< Y, !, merge(Xs, [Y| Ys], Zs).
merge([X| Xs], [Y| Ys], [Y| Zs]) :-
X @> Y, !, merge([X | Xs], Ys, Zs).
merge([], Xs, Xs) :- !. merge(Xs, [], Xs).</lang>
Lua
<lang Lua>function getLower(a,b)
local i,j=1,1
return function()
if not b[j] or a[i] and a[i]<b[j] then
i=i+1; return a[i-1]
else
j=j+1; return b[j-1]
end
end
end
function merge(a,b)
local res={}
for v in getLower(a,b) do res[#res+1]=v end
return res
end
function mergesort(list)
if #list<=1 then return list end
local s=math.floor(#list/2)
return merge(mergesort{unpack(list,1,s)}, mergesort{unpack(list,s+1)})
end</lang>
Lucid
[1] <lang lucid>msort(a) = if iseod(first next a) then a else merge(msort(b0),msort(b1)) fi
where
p = false fby not p;
b0 = a whenever p;
b1 = a whenever not p;
just(a) = ja
where
ja = a fby if iseod ja then eod else next a fi;
end;
merge(x,y) = if takexx then xx else yy fi
where
xx = (x) upon takexx;
yy = (y) upon not takexx;
takexx = if iseod(yy) then true elseif
iseod(xx) then false else xx <= yy fi;
end;
end;</lang>
Mathematica / Wolfram Language
<lang Mathematica>MergeSort[m_List] := Module[{middle},
If[Length[m] >= 2,
middle = Ceiling[Length[m]/2];
Apply[Merge,
Map[MergeSort, Partition[m, middle, middle, {1, 1}, {}]]],
m
]
]
Merge[left_List, right_List] := Module[
{leftIndex = 1, rightIndex = 1},
Table[
Which[
leftIndex > Length[left], rightrightIndex++,
rightIndex > Length[right], leftleftIndex++,
leftleftIndex <= rightrightIndex, leftleftIndex++,
True, rightrightIndex++],
{Length[left] + Length[right]}]
]</lang>
MATLAB
<lang MATLAB>function list = mergeSort(list)
if numel(list) <= 1
return
else
middle = ceil(numel(list) / 2);
left = list(1:middle);
right = list(middle+1:end);
left = mergeSort(left);
right = mergeSort(right);
if left(end) <= right(1)
list = [left right];
return
end
%merge(left,right)
counter = 1;
while (numel(left) > 0) && (numel(right) > 0)
if(left(1) <= right(1))
list(counter) = left(1);
left(1) = [];
else
list(counter) = right(1);
right(1) = [];
end
counter = counter + 1;
end
if numel(left) > 0
list(counter:end) = left;
elseif numel(right) > 0
list(counter:end) = right;
end
%end merge
end %if
end %mergeSort</lang> Sample Usage: <lang MATLAB>>> mergeSort([4 3 1 5 6 2])
ans =
1 2 3 4 5 6</lang>
Maxima
<lang maxima>merge(a, b) := block(
[c: [ ], i: 1, j: 1, p: length(a), q: length(b)],
while i <= p and j <= q do (
if a[i] < b[j] then (
c: endcons(a[i], c),
i: i + 1
) else (
c: endcons(b[j], c),
j: j + 1
)
),
if i > p then append(c, rest(b, j - 1)) else append(c, rest(a, i - 1))
)$
mergesort(u) := block(
[n: length(u), k, a, b],
if n <= 1 then u else (
a: rest(u, k: quotient(n, 2)),
b: rest(u, k - n),
merge(mergesort(a), mergesort(b))
)
)$</lang>
MAXScript
<lang MAXScript>fn mergesort arr = ( local left = #() local right = #() local result = #() if arr.count < 2 then return arr else ( local mid = arr.count/2 for i = 1 to mid do ( append left arr[i] ) for i = (mid+1) to arr.count do ( append right arr[i] ) left = mergesort left right = mergesort right if left[left.count] <= right[1] do ( join left right return left ) result = _merge left right return result ) )
fn _merge a b = ( local result = #() while a.count > 0 and b.count > 0 do ( if a[1] <= b[1] then ( append result a[1] a = for i in 2 to a.count collect a[i] ) else ( append result b[1] b = for i in 2 to b.count collect b[i] ) ) if a.count > 0 do ( join result a ) if b.count > 0 do ( join result b ) return result )</lang> Output: <lang MAXScript> a = for i in 1 to 15 collect random -5 20
- (-3, 13, 2, -2, 13, 9, 17, 7, 16, 19, 0, 0, 20, 18, 1)
mergeSort a
- (-3, -2, 0, 0, 1, 2, 7, 9, 13, 13, 16, 17, 18, 19, 20)
</lang>
Mercury
This version of a sort will sort a list of any type for which there is an ordering predicate defined. Both a function form and a predicate form are defined here with the function implemented in terms of the predicate. Some of the ceremony has been elided. <lang mercury>
- - module merge_sort.
- - interface.
- - import_module list.
- - type split_error ---> split_error.
- - func merge_sort(list(T)) = list(T).
- - pred merge_sort(list(T)::in, list(T)::out) is det.
- - implementation.
- - import_module int, exception.
merge_sort(U) = S :- merge_sort(U, S).
merge_sort(U, S) :- merge_sort(list.length(U), U, S).
- - pred merge_sort(int::in, list(T)::in, list(T)::out) is det.
merge_sort(L, U, S) :-
( L > 1 ->
H = L // 2,
( split(H, U, F, B) ->
merge_sort(H, F, SF),
merge_sort(L - H, B, SB),
merge_sort.merge(SF, SB, S)
; throw(split_error) )
; S = U ).
- - pred split(int::in, list(T)::in, list(T)::out, list(T)::out) is semidet.
split(N, L, S, E) :-
( N = 0 -> S = [], E = L
; N > 0, L = [H | L1], S = [H | S1],
split(N - 1, L1, S1, E) ).
- - pred merge(list(T)::in, list(T)::in, list(T)::out) is det.
merge([], [], []). merge([X|Xs], [], [X|Xs]). merge([], [Y|Ys], [Y|Ys]). merge([X|Xs], [Y|Ys], M) :-
( compare(>, X, Y) ->
merge_sort.merge([X|Xs], Ys, M0),
M = [Y|M0]
; merge_sort.merge(Xs, [Y|Ys], M0),
M = [X|M0] ).
</lang>
Nim
<lang nim>proc merge[T](a, b: var openarray[T], left, middle, right) =
let leftLen = middle - left rightLen = right - middle var l = 0 r = leftLen
for i in left .. <middle: b[l] = a[i] inc l for i in middle .. < right: b[r] = a[i] inc r
l = 0 r = leftLen var i = left
while l < leftLen and r < leftLen + rightLen:
if b[l] < b[r]:
a[i] = b[l]
inc l
else:
a[i] = b[r]
inc r
inc i
while l < leftLen: a[i] = b[l] inc l inc i while r < leftLen + rightLen: a[i] = b[r] inc r inc i
proc mergeSort[T](a, b: var openarray[T], left, right) =
if right - left <= 1: return
let middle = (left + right) div 2 mergeSort(a, b, left, middle) mergeSort(a, b, middle, right) merge(a, b, left, middle, right)
proc mergeSort[T](a: var openarray[T]) =
var b = newSeq[T](a.len) mergeSort(a, b, 0, a.len)
var a = @[4, 65, 2, -31, 0, 99, 2, 83, 782] mergeSort a echo a</lang>
- Output:
@[-31, 0, 2, 2, 4, 65, 83, 99, 782]
OCaml
<lang ocaml>let rec split_at n xs =
match n, xs with
0, xs ->
[], xs
| _, [] ->
failwith "index too large"
| n, x::xs when n > 0 ->
let xs', xs = split_at (pred n) xs in
x::xs', xs
| _, _ ->
invalid_arg "negative argument"
let rec merge_sort cmp = function
[] -> []
| [x] -> [x]
| xs ->
let xs, ys = split_at (List.length xs / 2) xs in
List.merge cmp (merge_sort cmp xs) (merge_sort cmp ys)
let _ =
merge_sort compare [8;6;4;2;1;3;5;7;9]</lang>
Oz
<lang oz>declare
fun {MergeSort Xs}
case Xs
of nil then nil
[] [X] then [X]
else
Middle = {Length Xs} div 2
Left Right
{List.takeDrop Xs Middle ?Left ?Right}
in
{List.merge {MergeSort Left} {MergeSort Right} Value.'<'}
end
end
in
{Show {MergeSort [3 1 4 1 5 9 2 6 5]}}</lang>
Nemerle
This is a translation of a Standard ML example from Wikipedia. <lang Nemerle>using System; using System.Console; using Nemerle.Collections;
module Mergesort {
MergeSort[TEnu, TItem] (sort_me : TEnu) : list[TItem]
where TEnu : Seq[TItem]
where TItem : IComparable
{
def split(xs) {
def loop (zs, xs, ys) {
|(x::y::zs, xs, ys) => loop(zs, x::xs, y::ys)
|(x::[], xs, ys) => (x::xs, ys)
|([], xs, ys) => (xs, ys)
}
loop(xs, [], [])
}
def merge(xs, ys) {
def loop(res, xs, ys) {
|(res, [], []) => res.Reverse()
|(res, x::xs, []) => loop(x::res, xs, [])
|(res, [], y::ys) => loop(y::res, [], ys)
|(res, x::xs, y::ys) => if (x.CompareTo(y) < 0) loop(x::res, xs, y::ys)
else loop(y::res, x::xs, ys)
}
loop ([], xs, ys)
}
def ms(xs) {
|[] => []
|[x] => [x]
|_ => { def (left, right) = split(xs); merge(ms(left), ms(right)) }
}
ms(sort_me.NToList())
}
Main() : void
{
def test1 = MergeSort([1, 5, 9, 2, 7, 8, 4, 6, 3]);
def test2 = MergeSort(array['a', 't', 'w', 'f', 'c', 'y', 'l']);
WriteLine(test1);
WriteLine(test2);
}
}</lang>
- Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9] [a, c, f, l, t, w, y]
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary
import java.util.List
placesList = [String -
"UK London", "US New York", "US Boston", "US Washington" - , "UK Washington", "US Birmingham", "UK Birmingham", "UK Boston" -
]
lists = [ -
placesList - , mergeSort(String[] Arrays.copyOf(placesList, placesList.length)) -
]
loop ln = 0 to lists.length - 1
cl = lists[ln] loop ct = 0 to cl.length - 1 say cl[ct] end ct say end ln
return
method mergeSort(m = String[]) public constant binary returns String[]
rl = String[m.length] al = List mergeSort(Arrays.asList(m)) al.toArray(rl)
return rl
method mergeSort(m = List) public constant binary returns ArrayList
result = ArrayList(m.size)
left = ArrayList()
right = ArrayList()
if m.size > 1 then do
middle = m.size % 2
loop x_ = 0 to middle - 1
left.add(m.get(x_))
end x_
loop x_ = middle to m.size - 1
right.add(m.get(x_))
end x_
left = mergeSort(left)
right = mergeSort(right)
if (Comparable left.get(left.size - 1)).compareTo(Comparable right.get(0)) <= 0 then do
left.addAll(right)
result.addAll(m)
end
else do
result = merge(left, right)
end
end
else do
result.addAll(m)
end
return result
method merge(left = List, right = List) public constant binary returns ArrayList
result = ArrayList()
loop label mx while left.size > 0 & right.size > 0
if (Comparable left.get(0)).compareTo(Comparable right.get(0)) <= 0 then do
result.add(left.get(0))
left.remove(0)
end
else do
result.add(right.get(0))
right.remove(0)
end
end mx
if left.size > 0 then do
result.addAll(left)
end
if right.size > 0 then do
result.addAll(right)
end
return result
</lang>
- Output:
UK London US New York US Boston US Washington UK Washington US Birmingham UK Birmingham UK Boston UK Birmingham UK Boston UK London UK Washington US Birmingham US Boston US New York US Washington
PARI/GP
Note also that the built-in vecsort and listsort use a merge sort internally.
<lang parigp>mergeSort(v)={
if(#v<2, return(v)); my(m=#v\2,left=vector(m,i,v[i]),right=vector(#v-m,i,v[m+i])); left=mergeSort(left); right=mergeSort(right); merge(left, right)
}; merge(u,v)={ my(ret=vector(#u+#v),i=1,j=1); for(k=1,#ret, if(i<=#u & (j>#v | u[i]<v[j]), ret[k]=u[i]; i++ , ret[k]=v[j]; j++ ) ); ret };</lang>
Pascal
<lang pascal>program MergeSortDemo;
type
TIntArray = array of integer;
function merge(left, right: TIntArray): TIntArray;
var
i, j: integer;
begin
j := 0;
setlength(merge, length(left) + length(right));
while (length(left) > 0) and (length(right) > 0) do
begin
if left[0] <= right[0] then
begin
merge[j] := left[0]; inc(j); for i := low(left) to high(left) - 1 do left[i] := left[i+1]; setlength(left, length(left) - 1);
end
else
begin
merge[j] := right[0]; inc(j); for i := low(right) to high(right) - 1 do right[i] := right[i+1]; setlength(right, length(right) - 1);
end;
end;
if length(left) > 0 then
for i := low(left) to high(left) do
merge[j + i] := left[i];
j := j + length(left);
if length(right) > 0 then
for i := low(right) to high(right) do
merge[j + i] := right[i];
end;
function mergeSort(m: TIntArray): TIntArray;
var
left, right: TIntArray;
i, middle: integer;
begin
setlength(mergeSort, length(m));
if length(m) = 1 then
mergeSort[0] := m[0]
else if length(m) > 1 then
begin
middle := length(m) div 2;
setlength(left, middle);
setlength(right, length(m)-middle);
for i := low(left) to high(left) do
left[i] := m[i];
for i := low(right) to high(right) do
right[i] := m[middle+i];
left := mergeSort(left);
right := mergeSort(right);
mergeSort := merge(left, right);
end;
end;
var
data: TIntArray; i: integer;
begin
setlength(data, 8);
Randomize;
writeln('The data before sorting:');
for i := low(data) to high(data) do
begin
data[i] := Random(high(data));
write(data[i]:4);
end;
writeln;
data := mergeSort(data);
writeln('The data after sorting:');
for i := low(data) to high(data) do
begin
write(data[i]:4);
end;
writeln;
end.</lang>
- Output:
./MergeSort The data before sorting: 6 1 2 1 5 2 1 5 The data after sorting: 1 1 1 2 2 5 5 6
improvement
uses "only" one halfsized temporary array for merging, which are set to the right size in before. small sized fields are sorted via insertion sort. Only an array of Pointers is sorted, so no complex data transfers are needed.Sort for X,Y or whatever is easy to implement.
Works with ( Turbo -) Delphi too. <lang pascal>{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,Regvar,ASMCSE,CSE,PEEPHOLE}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils; //for timing
type
tDataElem = record
myText : AnsiString;
myX,
myY : double;
myTag,
myOrgIdx : LongInt;
end;
tpDataElem = ^tDataElem;
tData = array of tDataElem;
tSortData = array of tpDataElem;
tCompFunc = function(A,B:tpDataElem):integer;
var
Data : tData; Sortdata, tmpData : tSortData;
procedure InitData(var D:tData;cnt: LongWord); var
i,k: LongInt;
begin
Setlength(D,cnt);
Setlength(SortData,cnt);
Setlength(tmpData,cnt shr 1 +1 );
k := 10*cnt;
For i := cnt-1 downto 0 do
Begin
Sortdata[i] := @D[i];
with D[i] do
Begin
myText := Format('_%.9d',[random(cnt)+1]);
myX := Random*k;
myY := Random*k;
myTag := Random(k);
myOrgIdx := i;
end;
end;
end;
procedure FreeData(var D:tData); begin
Setlength(tmpData,0); Setlength(SortData,0); Setlength(D,0);
end;
function CompLowercase(A,B:tpDataElem):integer; var
lcA,lcB: String;
Begin
lcA := lowercase(A^.myText); lcB := lowercase(B^.myText); result := ORD(lcA > lcB)-ORD(lcA < lcB);
end;
function myCompText(A,B:tpDataElem):integer; {sort an array (or list) of strings in order of descending length,
and in ascending lexicographic order for strings of equal length.}
var
lA,lB:integer;
Begin
lA := Length(A^.myText); lB := Length(B^.myText); result := ORD(lA<lB)-ORD(lA>lB); IF result = 0 then result := CompLowercase(A,B);
end;
function myCompX(A,B:tpDataElem):integer; //same as sign without jumps in assembler code begin
result := ORD(A^.myX > B^.myX)-ORD(A^.myX < B^.myX);
end;
function myCompY(A,B:tpDataElem):integer; Begin
result := ORD(A^.myY > B^.myY)-ORD(A^.myY < B^.myY);
end;
function myCompTag(A,B:tpDataElem):integer; Begin
result := ORD(A^.myTag > B^.myTag)-ORD(A^.myTag < B^.myTag);
end;
procedure InsertionSort(left,right:integer;var a: tSortData;CompFunc: tCompFunc); var
Pivot : tpDataElem; i,j : LongInt;
begin
for i:=left+1 to right do
begin
j :=i;
Pivot := A[j];
while (j>left) AND (CompFunc(A[j-1],Pivot)>0) do
begin
A[j] := A[j-1];
dec(j);
end;
A[j] :=PiVot;// s.o.
end;
end;
procedure mergesort(left,right:integer;var a: tSortData;CompFunc: tCompFunc);
var
i,j,k,mid :integer;
begin {// without insertion sort
If right>left then
} //{ test insertion sort
If right-left<=14 then
InsertionSort(left,right,a,CompFunc)
else
//}
begin
//recursion
mid := (right+left) div 2;
mergesort(left, mid,a,CompFunc);
mergesort(mid+1, right,a,CompFunc);
//already sorted ?
IF CompFunc(A[Mid],A[Mid+1])<0 then
exit;
//########## Merge ##########
//copy lower half to temporary array
move(A[left],tmpData[0],(mid-left+1)*SizeOf(Pointer));
i := 0;
j := mid+1;
k := left;
// re-integrate
while (k<j) AND (j<=right) do
begin
IF CompFunc(tmpData[i],A[j])<=0 then
begin
A[k] := tmpData[i];
inc(i);
end
else
begin
A[k]:= A[j];
inc(j);
end;
inc(k);
end;
//the rest of tmpdata a move should do too, in next life
while (k<j) do
begin
A[k] := tmpData[i];
inc(i);
inc(k);
end;
end;
end;
var
T1,T0: TDateTime; i : integer;
Begin
randomize;
InitData(Data,1*1000*1000);
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompText);
T1 := Time;
Writeln('myText ',FormatDateTime('NN:SS.ZZZ',T1-T0));
// For i := 0 to High(Data) do Write(SortData[i].myText); writeln;
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompX);
T1 := Time;
Writeln('myX ',FormatDateTime('NN:SS.ZZZ',T1-T0));
//check
For i := 1 to High(Data) do
IF myCompX(SortData[i-1],SortData[i]) = 1 then
Write(i:8);
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompY);
T1 := Time;
Writeln('myY ',FormatDateTime('NN:SS.ZZZ',T1-T0));
T0 := Time;
mergesort(Low(SortData),High(SortData),SortData,@myCompTag);
T1 := Time;
Writeln('myTag ',FormatDateTime('NN:SS.ZZZ',T1-T0));
FreeData (Data);
end. </lang>
- output
Free pascal 2.6.4 32bit / Win7 / i 4330 3.5 Ghz myText 00:03.158 / nearly worst case , all strings same sized and starting with '_000..' myX 00:00.360 myY 00:00.363 myTag 00:00.283
Perl
<lang perl>sub merge_sort {
my @x = @_;
return @x if @x < 2;
my $m = int @x / 2;
my @a = merge_sort(@x[0 .. $m - 1]);
my @b = merge_sort(@x[$m .. $#x]);
for (@x) {
$_ = !@a ? shift @b
: !@b ? shift @a
: $a[0] <= $b[0] ? shift @a
: shift @b;
}
@x;
}
my @a = (4, 65, 2, -31, 0, 99, 83, 782, 1); @a = merge_sort @a; print "@a\n";</lang> Also note, the built-in function sort uses mergesort.
Perl 6
<lang perl6>sub merge_sort ( @a ) {
return @a if @a <= 1;
my $m = @a.elems div 2; my @l = flat merge_sort @a[ 0 ..^ $m ]; my @r = flat merge_sort @a[ $m ..^ @a ];
return flat @l, @r if @l[*-1] !after @r[0];
return flat gather {
take @l[0] before @r[0] ?? @l.shift !! @r.shift
while @l and @r;
take @l, @r;
}
} my @data = 6, 7, 2, 1, 8, 9, 5, 3, 4; say 'input = ' ~ @data; say 'output = ' ~ @data.&merge_sort;</lang>
- Output:
input = 6 7 2 1 8 9 5 3 4 output = 1 2 3 4 5 6 7 8 9
Phix
Copy of Euphoria <lang Phix>function merge(sequence left, sequence right) sequence result = {}
while length(left)>0 and length(right)>0 do
if left[1]<=right[1] then
result = append(result, left[1])
left = left[2..$]
else
result = append(result, right[1])
right = right[2..$]
end if
end while
return result & left & right
end function
function mergesort(sequence m) sequence left, right integer middle
if length(m)<=1 then
return m
end if
middle = floor(length(m)/2)
left = mergesort(m[1..middle])
right = mergesort(m[middle+1..$])
if left[$]<=right[1] then
return left & right
elsif right[$]<=left[1] then
return right & left
end if
return merge(left, right)
end function
constant s = shuffle(tagset(10)) ? s ? mergesort(s) </lang>
- Output:
{8,1,2,5,10,3,9,6,7,4}
{1,2,3,4,5,6,7,8,9,10}
PHP
<lang php>function mergesort($arr){ if(count($arr) == 1 ) return $arr; $mid = count($arr) / 2;
$left = array_slice($arr, 0, $mid); $right = array_slice($arr, $mid);
$left = mergesort($left); $right = mergesort($right); return merge($left, $right); }
function merge($left, $right){ $res = array(); while (count($left) > 0 && count($right) > 0){ if($left[0] > $right[0]){ $res[] = $right[0]; $right = array_slice($right , 1); }else{ $res[] = $left[0]; $left = array_slice($left, 1); } } while (count($left) > 0){ $res[] = $left[0]; $left = array_slice($left, 1); } while (count($right) > 0){ $res[] = $right[0]; $right = array_slice($right, 1); } return $res; }
$arr = array( 1, 5, 2, 7, 3, 9, 4, 6, 8); $arr = mergesort($arr); echo implode(',',$arr);</lang>
- Output:
1,2,3,4,5,6,7,8,9
PicoLisp
PicoLisp's built-in sort routine uses merge sort. This is a high level implementation. <lang lisp>(de alt (List)
(if List (cons (car List) (alt (cddr List))) ()) )
(de merge (L1 L2)
(cond
((not L2) L1)
((< (car L1) (car L2))
(cons (car L1) (merge L2 (cdr L1))))
(T (cons (car L2) (merge L1 (cdr L2)))) ) )
(de mergesort (List)
(if (cdr List)
(merge (mergesort (alt List)) (mergesort (alt (cdr List))))
List) )
(mergesort (8 1 5 3 9 0 2 7 6 4))</lang>
PL/I
<lang pli>MERGE: PROCEDURE (A,LA,B,LB,C);
/* Merge A(1:LA) with B(1:LB), putting the result in C
B and C may share the same memory, but not with A.
- /
DECLARE (A(*),B(*),C(*)) BYADDR POINTER; DECLARE (LA,LB) BYVALUE NONASGN FIXED BIN(31); DECLARE (I,J,K) FIXED BIN(31); DECLARE (SX) CHAR(58) VAR BASED (PX); DECLARE (SY) CHAR(58) VAR BASED (PY); DECLARE (PX,PY) POINTER;
I=1; J=1; K=1;
DO WHILE ((I <= LA) & (J <= LB));
PX=A(I); PY=B(J);
IF(SX <= SY) THEN
DO; C(K)=A(I); K=K+1; I=I+1; END;
ELSE
DO; C(K)=B(J); K=K+1; J=J+1; END;
END;
DO WHILE (I <= LA);
C(K)=A(I); I=I+1; K=K+1;
END;
RETURN;
END MERGE;
MERGESORT: PROCEDURE (AP,N) RECURSIVE ;
/* Sort the array AP containing N pointers to strings */
DECLARE (AP(*)) BYADDR POINTER;
DECLARE (N) BYVALUE NONASGN FIXED BINARY(31);
DECLARE (M,I) FIXED BINARY;
DECLARE AMP1(1) POINTER BASED(PAM);
DECLARE (pX,pY,PAM) POINTER;
DECLARE SX CHAR(58) VAR BASED(pX);
DECLARE SY CHAR(58) VAR BASED(pY);
IF (N=1) THEN RETURN; M = trunc((N+1)/2); IF (M>1) THEN CALL MERGESORT(AP,M); PAM=ADDR(AP(M+1)); IF (N-M > 1) THEN CALL MERGESORT(AMP1,N-M); pX=AP(M); pY=AP(M+1); IF SX <= SY then return; /* Skip Merge */ DO I=1 to M; TP(I)=AP(I); END; CALL MERGE(TP,M,AMP1,N-M,AP); RETURN;
END MERGESORT;</lang>
PowerShell
<lang PowerShell> function MergeSort([object[]] $SortInput) { # The base case exits for minimal lists that are sorted by definition if ($SortInput.Length -le 1) {return $SortInput}
# Divide and conquer [int] $midPoint = $SortInput.Length/2 # The @() operators ensure a single result remains typed as an array [object[]] $left = @(MergeSort @($SortInput[0..($midPoint-1)])) [object[]] $right = @(MergeSort @($SortInput[$midPoint..($SortInput.Length-1)]))
# Merge [object[]] $result = @() while (($left.Length -gt 0) -and ($right.Length -gt 0)) { if ($left[0] -lt $right[0]) { $result += $left[0] # Use an if/else rather than accessing the array range as $array[1..0] if ($left.Length -gt 1){$left = $left[1..$($left.Length-1)]} else {$left = @()} } else { $result += $right[0] # Without the if/else, $array[1..0] would return the whole array when $array.Length == 1 if ($right.Length -gt 1){$right = $right[1..$($right.Length-1)]} else {$right = @()} } }
# If we get here, either $left or $right is an empty array (or both are empty!). Since the # rest of the unmerged array is already sorted, we can simply string together what we have. # This line outputs the concatenated result. An explicit 'return' statement is not needed. $result + $left + $right } </lang>
Prolog
<lang prolog>% msort( L, S ) % True if S is a sorted copy of L, using merge sort msort( [], [] ). msort( [X], [X] ). msort( U, S ) :- split(U, L, R), msort(L, SL), msort(R, SR), merge(SL, SR, S).
% split( LIST, L, R ) % Alternate elements of LIST in L and R split( [], [], [] ). split( [X], [X], [] ). split( [L,R|T], [L|LT], [R|RT] ) :- split( T, LT, RT ).
% merge( LS, RS, M ) % Assuming LS and RS are sorted, True if M is the sorted merge of the two merge( [], RS, RS ). merge( LS, [], LS ). merge( [L|LS], [R|RS], [L|T] ) :- L =< R, merge( LS, [R|RS], T). merge( [L|LS], [R|RS], [R|T] ) :- L > R, merge( [L|LS], RS, T).</lang>
PureBasic
A non-optimized version with lists. <lang PureBasic>Procedure display(List m())
ForEach m()
Print(LSet(Str(m()), 3," "))
Next
PrintN("")
EndProcedure
- overwrites list m() with the merger of lists ma() and mb()
Procedure merge(List m(), List ma(), List mb())
FirstElement(m())
Protected ma_elementExists = FirstElement(ma())
Protected mb_elementExists = FirstElement(mb())
Repeat
If ma() <= mb()
m() = ma(): NextElement(m())
ma_elementExists = NextElement(ma())
Else
m() = mb(): NextElement(m())
mb_elementExists = NextElement(mb())
EndIf
Until Not (ma_elementExists And mb_elementExists)
If ma_elementExists
Repeat
m() = ma(): NextElement(m())
Until Not NextElement(ma())
ElseIf mb_elementExists
Repeat
m() = mb(): NextElement(m())
Until Not NextElement(mb())
EndIf
EndProcedure
Procedure mergesort(List m())
Protected NewList ma()
Protected NewList mb()
If ListSize(m()) > 1
Protected current, middle = (ListSize(m()) / 2 ) - 1
FirstElement(m())
While current <= middle
AddElement(ma())
ma() = m()
NextElement(m()): current + 1
Wend
PreviousElement(m())
While NextElement(m())
AddElement(mb())
mb() = m()
Wend
mergesort(ma())
mergesort(mb())
LastElement(ma()): FirstElement(mb())
If ma() <= mb()
FirstElement(m())
FirstElement(ma())
Repeat
m() = ma(): NextElement(m())
Until Not NextElement(ma())
Repeat
m() = mb(): NextElement(m())
Until Not NextElement(mb())
Else
merge(m(), ma(), mb())
EndIf
EndIf
EndProcedure
If OpenConsole()
Define i NewList x() For i = 1 To 21: AddElement(x()): x() = Random(60): Next display(x()) mergesort(x()) display(x()) Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang>
- Sample output:
22 51 31 59 58 45 11 2 16 56 38 42 2 10 23 41 42 25 45 28 42 2 2 10 11 16 22 23 25 28 31 38 41 42 42 42 45 45 51 56 58 59
Python
<lang python>from heapq import merge
def merge_sort(m):
if len(m) <= 1:
return m
middle = len(m) // 2 left = m[:middle] right = m[middle:]
left = merge_sort(left) right = merge_sort(right) return list(merge(left, right))</lang>
Pre-2.6, merge() could be implemented like this: <lang python>def merge(left, right):
result = []
left_idx, right_idx = 0, 0
while left_idx < len(left) and right_idx < len(right):
# change the direction of this comparison to change the direction of the sort
if left[left_idx] <= right[right_idx]:
result.append(left[left_idx])
left_idx += 1
else:
result.append(right[right_idx])
right_idx += 1
if left:
result.extend(left[left_idx:])
if right:
result.extend(right[right_idx:])
return result</lang>
R
<lang r>mergesort <- function(m) {
merge_ <- function(left, right)
{
result <- c()
while(length(left) > 0 && length(right) > 0)
{
if(left[1] <= right[1])
{
result <- c(result, left[1])
left <- left[-1]
} else
{
result <- c(result, right[1])
right <- right[-1]
}
}
if(length(left) > 0) result <- c(result, left)
if(length(right) > 0) result <- c(result, right)
result
}
len <- length(m)
if(len <= 1) m else
{
middle <- length(m) / 2
left <- m[1:floor(middle)]
right <- m[floor(middle+1):len]
left <- mergesort(left)
right <- mergesort(right)
if(left[length(left)] <= right[1])
{
c(left, right)
} else
{
merge_(left, right)
}
}
} mergesort(c(4, 65, 2, -31, 0, 99, 83, 782, 1)) # -31 0 1 2 4 65 83 99 782</lang>
Racket
<lang racket>
- lang racket
(define (merge xs ys)
(cond [(empty? xs) ys]
[(empty? ys) xs]
[(match* (xs ys)
[((list* a as) (list* b bs))
(cond [(<= a b) (cons a (merge as ys))]
[ (cons b (merge xs bs))])])]))
(define (merge-sort xs)
(match xs
[(or (list) (list _)) xs]
[_ (define-values (ys zs) (split-at xs (quotient (length xs) 2)))
(merge (merge-sort ys) (merge-sort zs))]))
</lang> This variation is bottom up: <lang racket>
- lang racket
(define (merge-sort xs)
(merge* (map list xs)))
(define (merge* xss)
(match xss
[(list) '()]
[(list xs) xss]
[(list xs ys zss ...)
(merge* (cons (merge xs ys) (merge* zss)))]))
(define (merge xs ys)
(cond [(empty? xs) ys]
[(empty? ys) xs]
[(match* (xs ys)
[((list* a as) (list* b bs))
(cond [(<= a b) (cons a (merge as ys))]
[ (cons b (merge xs bs))])])]))
</lang>
REBOL
msort: function [a compare] [msort-do merge] [
if (length? a) < 2 [return a]
; define a recursive Msort-do function
msort-do: function [a b l] [mid] [
either l < 4 [
if l = 3 [msort-do next b next a 2]
merge a b 1 next b l - 1
] [
mid: make integer! l / 2
msort-do b a mid
msort-do skip b mid skip a mid l - mid
merge a b mid skip b mid l - mid
]
]
; function Merge is the key part of the algorithm
merge: func [a b lb c lc] [
until [
either (compare first b first c) [
change/only a first b
b: next b
a: next a
zero? lb: lb - 1
] [
change/only a first c
c: next c
a: next a
zero? lc: lc - 1
]
]
loop lb [
change/only a first b
b: next b
a: next a
]
loop lc [
change/only a first c
c: next c
a: next a
]
]
msort-do a copy a length? a
a
]
REXX
Note: the array elements can be anything: integers, floating point (exponentiated), characters ... <lang rexx>/*REXX program sorts a stemmed array (numbers or chars) using the merge─sort algorithm.*/ @.=; @.1 = '---The seven deadly sins---'
@.2 = '===========================' ; @.6 = "envy"
@.3 = 'pride' ; @.7 = "gluttony"
@.4 = 'avarice' ; @.8 = "sloth"
@.5 = 'wrath' ; @.9 = "lust"
do #=1 while @.#\==; end; #=#-1; w=length(#) /*#≡number of entries in @*/
call show@ 'before sort' /*show the "before" array elements. */
say copies('▒', 70) /*display a separator line to the term.*/
call mergeSort # /*invoke the merge sort for the array*/ call show@ ' after sort' /*show the "after" array elements. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ mergeSort: procedure expose @.; call mergeTo@ 1,arg(1); return /*──────────────────────────────────────────────────────────────────────────────────────*/ mergeTo@: procedure expose @. !.; parse arg L,n; if n==1 then return; h=L+1
if n==2 then do; if @.L>@.h then do; _=@.h; @.h=@.L; @.L=_; end; return; end
m=n%2 /* [↑] handle case of two items.*/
call mergeTo@ L+m,n-m /*divide items to the left ···*/
call mergeTo! L,m,1 /* " " " " right ···*/
i=1; j=L+m; do k=L while k<j /*whilst items on right exist ···*/
if j==L+n | !.i<=@.j then do; @.k=!.i; i=i+1; end
else do; @.k=@.j; j=j+1; end
end /*k*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ mergeTo!: procedure expose @. !.; parse arg L,n,T; if n==1 then do; !.T=@.L; return; end
if n==2 then do; h=L+1; q=T+1; !.q=@.L; !.T=@.h; return; end
m=n%2 /* [↑] handle case of two items.*/
call mergeTo@ L,m /*divide items to the left ···*/
call mergeTo! L+m,n-m,m+T /* " " " " right ···*/
i=L; j=m+T; do k=T while k<j /*whilst items on left exist ···*/
if j==T+n | @.i<=!.j then do; !.k=@.i; i=i+1; end
else do; !.k=!.j; j=j+1; end
end /*k*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ show@: do j=1 for #; say right('element',17) right(j,w) arg(1)":" @.j; end; return</lang> output when using the default input:
element 1 before sort: ---The seven deadly sins---
element 2 before sort: ===========================
element 3 before sort: pride
element 4 before sort: avarice
element 5 before sort: wrath
element 6 before sort: envy
element 7 before sort: gluttony
element 8 before sort: sloth
element 9 before sort: lust
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
element 1 after sort: ---The seven deadly sins---
element 2 after sort: ===========================
element 3 after sort: avarice
element 4 after sort: envy
element 5 after sort: gluttony
element 6 after sort: lust
element 7 after sort: pride
element 8 after sort: sloth
element 9 after sort: wrath
Ruby
<lang ruby>def merge_sort(m)
return m if m.length <= 1 middle = m.length / 2 left = merge_sort(m[0...middle]) right = merge_sort(m[middle..-1]) merge(left, right)
end
def merge(left, right)
result = [] until left.empty? || right.empty? result << (left.first<=right.first ? left.shift : right.shift) end result + left + right
end
ary = [7,6,5,9,8,4,3,1,2,0] p merge_sort(ary) # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]</lang>
Here's a version that monkey patches the Array class, with an example that demonstrates it's a stable sort <lang ruby>class Array
def mergesort(&comparitor)
return self if length <= 1
comparitor ||= proc{|a, b| a <=> b}
middle = length / 2
left = self[0...middle].mergesort(&comparitor)
right = self[middle..-1].mergesort(&comparitor)
merge(left, right, comparitor)
end
private
def merge(left, right, comparitor)
result = []
until left.empty? || right.empty?
# change the direction of this comparison to change the direction of the sort
if comparitor[left.first, right.first] <= 0
result << left.shift
else
result << right.shift
end
end
result + left + right
end
end
ary = [7,6,5,9,8,4,3,1,2,0] p ary.mergesort # => [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] p ary.mergesort {|a, b| b <=> a} # => [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
ary = [["UK", "London"], ["US", "New York"], ["US", "Birmingham"], ["UK", "Birmingham"]] p ary.mergesort
- => [["UK", "Birmingham"], ["UK", "London"], ["US", "Birmingham"], ["US", "New York"]]
p ary.mergesort {|a, b| a[1] <=> b[1]}
- => [["US", "Birmingham"], ["UK", "Birmingham"], ["UK", "London"], ["US", "New York"]]</lang>
Rust
<lang rust> fn merge<T: Copy + PartialOrd>(x1: &[T], x2: &[T], y: &mut [T]) { assert_eq!(x1.len() + x2.len(), y.len()); let mut i = 0; let mut j = 0; let mut k = 0; while i < x1.len() && j < x2.len() { if x1[i] < x2[j] { y[k] = x1[i]; k += 1; i += 1; } else { y[k] = x2[j]; k += 1; j += 1; } } if i < x1.len() { y[k..].copy_from_slice(&x1[i..]); } if j < x2.len() { y[k..].copy_from_slice(&x2[j..]); } } </lang>
The sort algorithm : <lang rust> fn merge_sort_rec<T: Copy + Ord>(x: &mut [T]) { let n = x.len(); let m = n / 2;
if n <= 1 { return; }
merge_sort_rec(&mut x[0..m]); merge_sort_rec(&mut x[m..n]);
let mut y: Vec<T> = x.to_vec();
merge(&x[0..m], &x[m..n], &mut y[..]);
x.copy_from_slice(&y); } </lang>
Version without recursion call (faster) : <lang rust> fn merge_sort<T: Copy + PartialOrd>(x: &mut [T]) { let n = x.len(); let mut y = x.to_vec(); let mut len = 1; while len < n { let mut i = 0; while i < n { if i + len >= n { y[i..].copy_from_slice(&x[i..]); } else if i + 2 * len > n { merge(&x[i..i+len], &x[i+len..], &mut y[i..]); } else { merge(&x[i..i+len], &x[i+len..i+2*len], &mut y[i..i+2*len]); } i += 2 * len; } len *= 2; if len >= n { x.copy_from_slice(&y); return; } i = 0; while i < n { if i + len >= n { x[i..].copy_from_slice(&y[i..]); } else if i + 2 * len > n { merge(&y[i..i+len], &y[i+len..], &mut x[i..]); } else { merge(&y[i..i+len], &y[i+len..i+2*len], &mut x[i..i+2*len]); } i += 2 * len; } len *= 2; } } </lang>
Scala
The use of Stream as the merge result avoids stack overflows without resorting to tail recursion, which would typically require reversing the result, as well as being a bit more convoluted.
<lang scala>def mergeSort(input: List[Int]) = {
def merge(left: List[Int], right: List[Int]): Stream[Int] = (left, right) match {
case (x :: xs, y :: ys) if x <= y => x #:: merge(xs, right)
case (x :: xs, y :: ys) => y #:: merge(left, ys)
case _ => if (left.isEmpty) right.toStream else left.toStream
}
def sort(input: List[Int], length: Int): List[Int] = input match {
case Nil | List(_) => input
case _ =>
val middle = length / 2
val (left, right) = input splitAt middle
merge(sort(left, middle), sort(right, middle + length % 2)).toList
}
sort(input, input.length)
}</lang>
Replace the first two lines of merge by the following:
<lang scala> case (x :: xs, y :: ys) if x < y => Stream.cons(x, merge(xs, right))
case (x :: xs, y :: ys) => Stream.cons(y, merge(left, ys))</lang>
I suppose I should have written this version to begin with, but I think the 2.8 version is more clear.
Scheme
<lang scheme>(define (merge-sort l gt?)
(define (merge left right)
(cond
((null? left)
right)
((null? right)
left)
((gt? (car left) (car right))
(cons (car right)
(merge left (cdr right))))
(else
(cons (car left)
(merge (cdr left) right)))))
(define (take l n)
(if (zero? n)
(list)
(cons (car l)
(take (cdr l) (- n 1)))))
(let ((half (quotient (length l) 2)))
(if (zero? half)
l
(merge (merge-sort (take l half) gt?)
(merge-sort (list-tail l half) gt?)))))</lang>
(merge-sort '(1 3 5 7 9 8 6 4 2) >)
Seed7
<lang seed7>const proc: mergeSort2 (inout array elemType: arr, in integer: lo, in integer: hi, inout array elemType: scratch) is func
local
var integer: mid is 0;
var integer: k is 0;
var integer: t_lo is 0;
var integer: t_hi is 0;
begin
if lo < hi then
mid := (lo + hi) div 2;
mergeSort2(arr, lo, mid, scratch);
mergeSort2(arr, succ(mid), hi, scratch);
t_lo := lo;
t_hi := succ(mid);
for k range lo to hi do
if t_lo <= mid and (t_hi > hi or arr[t_lo] <= arr[t_hi]) then
scratch[k] := arr[t_lo];
incr(t_lo);
else
scratch[k] := arr[t_hi];
incr(t_hi);
end if;
end for;
for k range lo to hi do
arr[k] := scratch[k];
end for;
end if;
end func;
const proc: mergeSort2 (inout array elemType: arr) is func
local var array elemType: scratch is 0 times elemType.value; begin scratch := length(arr) times elemType.value; mergeSort2(arr, 1, length(arr), scratch); end func;</lang>
Original source: [2]
Sidef
<lang ruby>func merge(left, right) {
var result = [];
while (!left.is_empty && !right.is_empty) {
result.append([right,left][left.first <= right.first].shift);
};
result + left + right;
} func mergesort(array) {
var len = array.len; len < 2 && return array;
var mid = (len/2 -> int); var left = array.ft(0, mid-1); var right = array.ft(mid);
left = __FUNC__(left); right = __FUNC__(right);
merge(left, right);
}
- Numeric sort
var nums = (0..7 -> shuffle); say mergesort(nums);
- String sort
var strings = ('a'..'e' -> shuffle); say mergesort(strings);</lang>
- Output:
[0, 1, 2, 3, 4, 5, 6, 7] ['a', 'b', 'c', 'd', 'e']
Standard ML
<lang sml>fun merge cmp ([], ys) = ys
| merge cmp (xs, []) = xs
| merge cmp (xs as x::xs', ys as y::ys') =
case cmp (x, y) of GREATER => y :: merge cmp (xs, ys')
| _ => x :: merge cmp (xs', ys)
fun merge_sort cmp [] = []
| merge_sort cmp [x] = [x]
| merge_sort cmp xs = let
val ys = List.take (xs, length xs div 2)
val zs = List.drop (xs, length xs div 2)
in
merge cmp (merge_sort cmp ys, merge_sort cmp zs)
end
merge_sort Int.compare [8,6,4,2,1,3,5,7,9]</lang>
Swift
<lang Swift>func mergeSort<T:Comparable>(inout list:[T]) {
if list.count <= 1 {
return
}
func merge(var left:[T], var right:[T]) -> [T] {
var result = [T]()
while left.count != 0 && right.count != 0 {
if left[0] <= right[0] {
result.append(left.removeAtIndex(0))
} else {
result.append(right.removeAtIndex(0))
}
}
while left.count != 0 {
result.append(left.removeAtIndex(0))
}
while right.count != 0 {
result.append(right.removeAtIndex(0))
}
return result
}
var left = [T]()
var right = [T]()
let mid = list.count / 2
for i in 0..<mid {
left.append(list[i])
}
for i in mid..<list.count {
right.append(list[i])
}
mergeSort(&left)
mergeSort(&right)
list = merge(left, right)
}</lang>
Tcl
<lang tcl>package require Tcl 8.5
proc mergesort m {
set len [llength $m]
if {$len <= 1} {
return $m
}
set middle [expr {$len / 2}]
set left [lrange $m 0 [expr {$middle - 1}]]
set right [lrange $m $middle end]
return [merge [mergesort $left] [mergesort $right]]
}
proc merge {left right} {
set result [list]
while {[set lleft [llength $left]] > 0 && [set lright [llength $right]] > 0} {
if {[lindex $left 0] <= [lindex $right 0]} {
set left [lassign $left value]
} else {
set right [lassign $right value]
}
lappend result $value
}
if {$lleft > 0} {
lappend result {*}$left
}
if {$lright > 0} {
set result [concat $result $right] ;# another way append elements
}
return $result
}
puts [mergesort {8 6 4 2 1 3 5 7 9}] ;# => 1 2 3 4 5 6 7 8 9</lang> Also note that Tcl's built-in lsort command uses the mergesort algorithm.
UnixPipes
<lang bash>split() {
(while read a b ; do
echo $a > $1 ; echo $b > $2
done)
}
mergesort() {
xargs -n 2 | (read a b; test -n "$b" && (
lc="1.$1" ; gc="2.$1"
(echo $a $b;cat)|split >(mergesort $lc >$lc) >( mergesort $gc >$gc)
sort -m $lc $gc
rm -f $lc $gc;
) || echo $a)
}
cat to.sort | mergesort</lang>
Ursala
<lang Ursala>#import std
mergesort "p" = @iNCS :-0 ~&B^?a\~&YaO "p"?abh/~&alh2faltPrXPRC ~&arh2falrtPXPRC
- show+
example = mergesort(lleq) <'zoh','zpb','hhh','egi','bff','cii','yid'></lang>
- Output:
bff cii egi hhh yid zoh zpb
The mergesort function could also have been defined using the built in sorting operator, -<, because the same algorithm is used. <lang Ursala>mergesort "p" = "p"-<</lang>
V
merge uses the helper mergei to merge two lists. The mergei takes a stack of the form [mergedlist] [list1] [list2] it then extracts one element from list2, splits the list1 with it, joins the older merged list, first part of list1 and the element that was used for splitting (taken from list2) into the new merged list. the new list1 is the second part of the split on older list1. new list2 is the list remaining after the element e2 was extracted from it. <lang v>[merge
[mergei
uncons [swap [>] split] dip
[[*m] e2 [*a1] b1 a2 : [*m *a1 e2] b1 a2] view].
[a b : [] a b] view
[size zero?] [pop concat]
[mergei]
tailrec].
[msort
[splitat [arr a : [arr a take arr a drop]] view i]. [splitarr dup size 2 / >int splitat].
[small?] [] [splitarr] [merge] binrec].</lang>
[8 7 6 5 4 2 1 3 9] msort puts
XPL0
This is based on an example in "Fundamentals of Computer Algorithms" by Horowitz & Sahni. <lang XPL0>code Reserve=3, ChOut=8, IntOut=11;
proc MergeSort(A, Low, High); \Sort array A from Low to High int A, Low, High; int B, Mid, H, I, J, K; [if Low >= High then return; Mid:= (Low+High) >> 1; \split array in half (roughly) MergeSort(A, Low, Mid); \sort left half MergeSort(A, Mid+1, High); \sort right half \Merge the two halves in to sorted order B:= Reserve((High-Low+1)*4); \reserve space for working array (4 bytes/int) H:= Low; I:= Low; J:= Mid+1; while H<=Mid & J<=High do \merge while both halves have items
if A(H) <= A(J) then [B(I):= A(H); I:= I+1; H:= H+1]
else [B(I):= A(J); I:= I+1; J:= J+1];
if H > Mid then \copy any remaining elements
for K:= J to High do [B(I):= A(K); I:= I+1]
else for K:= H to Mid do [B(I):= A(K); I:= I+1]; for K:= Low to High do A(K):= B(K); ];
int A, I; [A:= [3, 1, 4, 1, -5, 9, 2, 6, 5, 4]; MergeSort(A, 0, 10-1); for I:= 0 to 10-1 do [IntOut(0, A(I)); ChOut(0, ^ )]; ]</lang>
- Output:
-5 1 1 2 3 4 4 5 6 9
ZED
Source -> http://ideone.com/uZEPL4 Compiled -> http://ideone.com/SJ5EGu
This is a bottom up version of merge sort: <lang zed>(append) list1 list2 comment:
- true
(003) "append" list1 list2
(car) pair comment:
- true
(002) "car" pair
(cdr) pair comment:
- true
(002) "cdr" pair
(cons) one two comment:
- true
(003) "cons" one two
(map) function list comment:
- true
(003) "map" function list
(merge) comparator list1 list2 comment:
- true
(merge1) comparator list1 list2 nil
(merge1) comparator list1 list2 collect comment: (null?) list2 (append) (reverse) collect list1
(merge1) comparator list1 list2 collect comment: (null?) list1 (append) (reverse) collect list2
(merge1) comparator list1 list2 collect comment: (003) comparator (car) list2 (car) list1 (merge1) comparator list1 (cdr) list2 (cons) (car) list2 collect
(merge1) comparator list1 list2 collect comment:
- true
(merge1) comparator (cdr) list1 list2 (cons) (car) list1 collect
(null?) value comment:
- true
(002) "null?" value
(reverse) list comment:
- true
(002) "reverse" list
(sort) comparator jumble comment:
- true
(car) (sort11) comparator (sort1) jumble
(sort1) jumble comment:
- true
(map) "list" jumble
(sort11) comparator jumble comment: (null?) jumble nil
(sort11) comparator jumble comment: (null?) (cdr) jumble jumble
(sort11) comparator jumble comment:
- true
(sort11) comparator
(cons) (merge) comparator (car) jumble (002) "cadr" jumble
(sort11) comparator (002) "cddr" jumble</lang>
zkl
Pretty wasteful memory wise, probably not suitable for large sorts.
<lang zkl>fcn _merge(left,right){
if (not left) return(right); if (not right) return(left); l:=left[0]; r:=right[0]; if (l<=r) return(L(l).extend(self.fcn(left[1,*],right))); else return(L(r).extend(self.fcn(left,right[1,*])));
}
fcn merge_sort(L){
if (L.len()<2) return(L); n:=L.len()/2; return(_merge(self.fcn(L[0,n]), self.fcn(L[n,*])));
}</lang> <lang zkl>merge_sort(T(1,3,5,7,9,8,6,4,2)).println(); merge_sort("big fjords vex quick waltz nymph").concat().println();</lang>
- Output:
L(1,2,3,4,5,6,7,8,9)
abcdefghiijklmnopqrstuvwxyz
Or, for lists only: <lang zkl>fcn mergeSort(L){
if (L.len()<2) return(L.copy()); n:=L.len()/2; self.fcn(L[0,n]).merge(self.fcn(L[n,*]));
}</lang> <lang zkl>mergeSort(T(1,3,5,7,9,8,6,4,2)).println(); mergeSort("big fjords vex quick waltz nymph".split("")).concat().println();</lang>
- Output:
L(1,2,3,4,5,6,7,8,9)
abcdefghiijklmnopqrstuvwxyz
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